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Can a concave polygon be regular? First, find the area of rectangle and square and then add the two areas to get the total area of a concave polygon. It can have sides of any length and each interior angle can be any measure. It also has no thickness to it. Concave polygon. $\endgroup$ – Adrian Keister Jan 21 '19 at 18:22 Also, the vertices of a concave polygon are both inwards and outwards. It looks sort of like a vertex has been 'pushed in' towards the inside of the polygon. These are those polygons that aren’t regular. A polygon is said to be regular if it has equal length on all of its sides and with equal angles at each vertex. Polygons can be studied and classified in many different ways. So a rectangle is convex. A concave or a convex polygon can be regular or irregular. The sum of interior angles of a regular polygon is 1080 degrees .What is the number of triangles the polygon can subdivide into geometry If the ratio of the interior angle to the exterior angle is 5:1 for a regular polygon, find a. the size of each exterior angle b. the number of sides of the polygon c. the sum of the interior angles d. Explain. A concave polygon is that under which at least one angle is recorded more than 180 degrees. A simple polygon is considered as a concave polygon if and only if at least one of the interior angles is greater than 1800. A regular polygon is a polygon that is both equiangular and equilateral. What regular polygons are used to design the soccer ball? False; to be concave the angles cannot be congruent. The sides of a polygon are segments that intersect exactly two other segments, one at … You should know the types of special polygons for your geometry test. Congruent Shapes are shapes that are simply the same, exactly equal in shape and size. This is an irregular concave pentagon. In a concave polygon, at least one of the interior angles is greater than [math]180[/math] degrees, like the second diagram below. What type of polygon is it? a.) Which polygon has an interior angle sum of 1080°? Angles that are on the inside of Polygon shapes are called interior or internal angles. Polygons with all interior angles less than 180° are convex; if a polygon has at least … A polygon can be regular or irregular. Convex polygon As you can see here, this irregular convex pentagon has 5 diagonals. NERDSTUDY.COM for more detailed lessons!What is a polygon? Also, the sum of the interior angles of a polygon is (n – 2) x 180, where n is the number of sides. A polygon is said to be irregular if its sides are not equal and angles differ from each other. So no interior angle is greater than  180°. Another way to think of it is this: the diagonals of a convex polygon will all be in the interior of the polygon, whereas certain diagonals of a concave polygon will lie outside the polygon, o… Stay tuned with BYJU’S – The Learning App and download the app to learn all the important Maths – related articles to learn with ease. Polygons also contain diagonals. (8 sides) Which polygon has an interior angle sum of 900°? A concave polygon is a polygon which is not convex. Officially, each interior angle in a convex polygon is less than 180° , and this is what makes all of the vertices point out. It must have at least four sides. A pentagon is a polygon that has five sides: A hexagon is a polygon with six sides: A heptagon is a polygon with seven sides: An octagon is a polygon with eight sides: A decagon is a polygon with ten sides: All of the polygons in the illustrations above are regular polygons. Diagonals are line segments joining two vertices that are not next to each other. A polygon can have anywhere between three and an unlimited number of sides. Slightly more information on planes, in addition to what we've introduced here, can be seen at the  mathopenref  website. A triangle cannot be considered as a concave polygon because it has only three sides and whose sum of interior angles is 180 degrees. A regular polygon is always convex. However if at least one interior angle of a Polygon is greater than, In the right Polygon above, the highlighted red interior angle is greater than, Combination Formula, Combinations without Repetition. When an equilateral polygon is non-crossing and cyclic (its vertices are on a circle) it must be regular. Convex polygons are the ones we're used to seeing the most: squares, triangles, pentagons, etc. Polygons can be studied and classified in many different ways. c.) False; all concave polygons are regular. An efficient algorithm for cutting off ears was discovered by Hossam ElGindy, Hazel Everett, and Godfried Toussaint. In a concave polygon, at least one of the interior angles is greater than [math]180[/math] degrees, like the second diagram below. Conjecture: They are vertical angles. It means that at least one of the interior angles is greater than 180° and less than 360°, If a line segment is drawn crossing the concave polygon, it will intersect the boundary more than two times, A polygon can have more than one diagonal that lie outside the boundary, A concave polygon has at least one pair of sides joining a vertex that goes outside the vertex, Square: n =4; sum of interior angles = 180 x (4-2) = 360 degrees, Pentagon: n = 5; sum of interior angles = 180 x (5-2) = 540 degrees, Hexagon: n = 6; sum of interior angles = 180 x (6-2) = 720 degrees. $\begingroup$ (from last comment) There are also other right pyramids that do not have a regular base but their lateral faces are still isosceles triangles, such as the rectangular right pyramid or the rhomboid pyramid. Find the area and perimeter for the concave polygon given below: In this figure, one of the shapes is rectangle and the other one is a square. Convex equilateral pentagon. A convex polygon is a simple polygon that has all its interior angles less than 18 0 ∘ 180^\circ 1 8 0 ∘ As opposed to a convex polygon, a concave polygon is a simple polygon that has at least one interior angle greater than 18 0 ∘ 180^\circ 1 8 0 ∘. Note that a triangle (3-gon) can never be concave. POLYGONS ASSIGNMENT Classify each of the following figures as concave polygon, convex polygon or not a An arrowhead is an example of a concave quadrilateral. An interior angle of a regular polygon has a measyre of 135°. An implementation that keeps separate lists of convex and concave vertices will run in O(n 2) time. A simple polygon … ... A regular polygon has all its sides equal and all its angles equal. Is Star a Concave Polygon? (In a concave polygon, some diagonals will lie outside the polygon). When they contain one or more internal angles with measurements greater than 180°, they are called concave. So for a regular Polygon, with  n  exterior angles, the size of one exterior angle angle can be found by: A Convex Polygon and a Concave Polygon are 2 different types of Polygons. It looks sort of like a vertex has been 'pushed in' towards the inside of the polygon.Note that a triangle (3-gon) can never be concave.A concave polygon is the opposite of a convex polygon.See Convex Polygon. False; to be concave the angles cannot be congruent. Explain. The area and perimeter of it will depend on the shape of the particular polygon. A polynomial-time algorithm for finding a decomposition into as few convex polygons as possible is described by Chazelle & Dobkin (1985). Polygons with congruent sides and angles are regular; all others are irregular. What is always the sum total of exterior angles? Concave Polygons. In the right Polygon above, the highlighted red interior angle is greater than  180°. NERDSTUDY.COM for more detailed lessons!What is a polygon? 2. Regular polygons are those that have equal sides and equal angles, that is, they are equilateral and equiangular. Can all polygons be represented at concave? Step 1: Find the area of the rectangle?Area of the rectangle = length x widthHere, length = 24 and width = 10Area = 24 x 10 = 240 sq units, Step 2: Find the area of the square?Area of square = Side x Side, Step 3: Total area of the concave polygon = Area of rectangle + Area of square, Step 4: Perimeter of given polygon = Sum of all sides. If any internal angle is greater than 180° then the polygon is concave. The polygon is not a concave polygon because of the followings two situations occur. Given: a concave polygon Conjecture: It can be regular or irregular 1 See answer melanddemond is waiting for your help. A polygon is a closed planar figure consisting of straight line segments.There are two types of polygons: convex and concave. A polygon is a two-dimensional shape that has straight lines. In the familiar Euclidean geometry, an equilateral … A regular polygon is a polygon where the length of each side is the same and all the interior angles are equal. Is there a polygon in which the sum … So no interior angle is greater than 180°. A concave polygon will always have an interior angle with a measure that is greater than 180 degrees. A simple line test can be used to distinguish a concave polygon with a convex polygon. One is partially outside and it is the black dotted line. Polygon shapes are flat 2D shapes that are closed, and made from straight lines. Though not a Polygon, a plane in Math is something worth mentioning here. Even if you drop the requirement of regularity, there cannot be a concave triangle. In a Convex Polygon, all points/vertices on the edge of the shape point outwards. A square is an example of a regular polygon… Examples include triangles, quadrilaterals, pentagons, hexagons and so on. A concave polygon is the opposite of a convex polygon. Polygons can be convex or concave. See Regular Polygon Definition. Regular or Irregular; Concave or Convex; Simple or Complex; Regular or Irregular Polygon. A Concave polygon is a polygon that has one or more interior angles greater than 180 degrees. 360. c. The pattern on a soccer … In a regular polygon, all sides and interior angles are equal. They … When you see an unfamiliar polygon, you can determine its properties and classify it correctly. Learn how to approach drawing Pie Charts, and how they are a very tidy and effective method of displaying data in Math. I don't know of any special term for that. Does the table represent a linear function? So generally, for a rectangle I would choose: d. … Regular Polygon: an equilateral, equiangular polygon. An irregular polygon is any polygon that is not a regular polygon.It can have sides of any length and each interior angle can be any measure. Concave Polygon, Convex Polygon. Conjecture: it can be regular or irregular. However if at least one interior angle of a Polygon is greater than  180°,  and as such pointing inwards, then the shape is a Concave Polygon. A regular convex polygon is a polygon where each side is of the same length, and all the interior angles are equal and less than 180 degrees. A polygon with any of the internal angles greater than 180 degrees is known as a concave polygon. A concave polygon has at least one angle that is > 180 degrees. The vertices and sides are evenly spread around a central point. If all sides are NOT the same length, and all angles inside are NOT all the same size, then the Polygon is irregular. An equilateral quadrilateral must be convex; this polygon is either a rhombus or a square. pentagon: 5: The simplest polygon which can exist as a regular star. See Convex Polygon. Equiangular polygons have congruent interior angles, like a rectangle. Hence, they point towards the interior of the polygon. All polygons with 4 or more sides can be concave. We begin with polygon … More precisely, no internal angle can be more than 180°. Four interior angles of an irregular pentagon measure 68, 176, 90 and 126. A concave polygon will always have an interior angle with a measure that is greater than 180 degrees. A polygon can be concave or convex ... Learn about polygons and how to classify them. Each side in a regular polygon is the same length as the other sides. In other words, a concave polygon exists with an interior reflex angle. A concave polygon cannot be regular because regularity requires all angles (and sides)to be of equal measure. A concave or a convex polygon can be regular or irregular. For a polygon to be convex, all of its interior angles must be less than 180 degrees. The perimeter of Concave Polygon = Sum of all its sides. Determine whether the conjecture is true or false. The sum of the interior angles formula of a polygon is given by: Sum of interior angles = 180 * (n – 2) degrees. A polygon with any of the internal angles greater than 180 degrees is known as a concave polygon. a. For an  n  sided regular Polygon, the sum of all the interior angles together can be given by the formula: 1)  Triangle  (3 sides)    =>    ( 3 − 2 ) × 180°  =  180°, 2)  Square  (4 sides)    =>    ( 4 − 2 ) × 180°  =  360°, 3)  Pentagon  (5 sides)    =>    ( 5 − 2 ) × 180°  =  540°. The irregular polygon can have sides with different measures and also each interior angles measures are also varied. A polygon has at least one angle that measures more than 180 degrees, which is called concave polygon. The area of an irregular convex polygon can be found by dividing it into triangles and summing the triangle's areas. A polygon is regular if all sides are the same length and all angles are congruent.. Equilateral triangle. One is completely outside and it is red dotted line. A regular Polygon is a Polygon in which all sides are the same length, and all angles inside are the same size. A Convex Polygon and a Concave Polygon are 2 different types of Polygons. Given:points R, S, and T Conjecture: R, S, And T are coplanar. Classify these polygons as convex, concave, or neither. It is noted that all the concave polygons are irregular since the interior angles of the polygon are of different measures. In their most general form, polygons are an ordered set of vertices, , , with edges joining consecutive vertices. Interior angle = 22° Exterior angle = 180° − 22° = 158° Such a polygon is not possible as 360° is not a perfect multiple of 158° The sides of a polygon are segments that intersect exactly two other segments, one at each endpoint. [citation needed] It is always possible to cut a concave polygon into a set of convex polygons. We are mainly concerned here about the shape, not about the lengths of sides. Section 5.3 Angles of Polygons 217 Solve the proportion. Hence, regular polygons are never concave. The right shape is closed, but is NOT formed by only straight edges/lines. Examples of such polygons are an isoceles triangle, a standard rectangle, and an irregular Pentagon. A Polygon has the same number of exterior angles as interior angles, the  5  exterior angles of the Polygon below are shown in red. Convex and Concave Polygon: A convex polygon has no angles pointing inwards. When you see an unfamiliar polygon, you can determine its properties and classify it correctly. A polygon is said to be regular if it has equal length on all of its sides and with equal angles at each vertex. Also, one or more interior angles should be greater than 180 degrees. An equilateral quadrilateral must be convex; this polygon is either a rhombus or a square. Equilateral polygons have congruent sides, like a rhombus. hexagon: 6 Can tile the plane. b. octagon. (In a convex polygon, all diagonals will lie inside the polygon). Yes. You now see that polygons can be regular or irregular, convex or concave, and simple or complex. View Polygons_Worksheet.docx from MATH 244 at York College, CUNY. Other 14. A polygon is a planeshape (two-dimensional) with straight sides. Convex Polygon. d. (7 sides) Which statements are true about polygons? Given: a concave polygon. 14 — 21 = … Those polygons are further classified into regular or irregular. A rectangle is equiangular (all angles are the same) A rectangle is not generally equilateral (all sides are the same) unless that rectangle is also a square. When an equilateral polygon is non-crossing and cyclic (its vertices are on a circle) it must be regular. A concave polygon is defined as a polygon with one or more interior angles greater than 180°. Regular vs Irregular... Convex vs Concave! Here is the list of some of the regular polygons with the number of polygon sides, shapes, and measures of its interior angles. The polygon above has 5 diagonals made with dotted lines. All of the lines of a polygon … They can be convex or concave, but all concave polygons are irregular since the interior angles cannot all be the same.If you drew a polygon at random, it would probably be irregular. Some Popular Polygons. The extension of at least one side or diagonal in a concave polygon will contain a point that is inside the polygon. As a polygon gets larger, what happens to the sum of the interior and exterior angles? All vertices in convex polygons point outward away from the center. Yes, a star is a concave polygon. The area of a concave polygon can be found by treating it as any other irregular polygon. Add your answer and earn points. A couple of exercises showing how to identify concave polygons by doing some math. In the figure on the right, the diagonal at the top of the polygon is outside the polygon's interior space. Rest of the detail can be read here.Beside this, how do you find the interior angle of a polygon? A polygon is a plane shape bounded by a finite chain of straight lines. 14. Square can be classified as -: a) Convex regular polygon b) Concave regular polygon c) Convex open polygon d) Concave open polygon No, triangles can't. 1.Given: a concave polygon Conjecture: it can be regular or irregular a) False, to be concave the angles cannot be congruent b)True c) False, all concave polygons are regular d) False, a concave polygon has as odd number of sides 2. (n-2)180. An irregular polygon is any polygon that is not a regular polygon. You now see that polygons can be regular or irregular, convex or concave, and simple or complex. For example, the interior angles of a pentagon always add up to 5400, no matter if it is convex or concave, or what size and shape it is. Regular Concave Polygon. a.) 1. In a regular Polygon such as the Pentagon above, all exterior anglers are the same size. "Note: There is at least one (1) interior angle pointing to a side of the polygon (the angle that exceeds 180 degrees). More precisely, no internal angle can be more than 180°. A regular polygon is a flat shape whose sides are all equal and whose angles are all equal. In an irregular polygon, the sides are not equal in length. A concave polygon has one or more of its vertices “pushed inside”. What is the formula for finding the sum total of the interior angles? Three of them are completely inside and these are the green, orange, and teal dotted lines. For a given number of side there exist both a regular concave polygon and a regular convex polygon? Look at the sides of the polygon in the example belo… A regular polygon is a polygon where the length of each side is the same and all the interior angles are equal. They are just opposite of the convex polygons. There are  3  or more points/vertices, joined by straight lines/edges. A polygon may be an either convex or concave polygon. Similarly, the perimeter of a concave polygon is defined as the total distance covered around the boundary of the concave polygon. Is the … A triangle is always convex polygon no matter which triangle it is. 6 A concave polygon is regular::never ===== Cheers, Stan H. Answer by Clara Oswin Oswald(1) (Show Source): You can put this solution on YOUR website! Concave polygon. A convex equilateral pentagon can be described by two … Concave polygon is a polygon that has one or more interior angles greater than 180° In a concave polygon, at least one diagonal of the figure contains points that are exterior to the polygon A line drawn through a concave polygon, can intersect the polygon in more than two points Concave polygon never bea regular polygon A concave polygon is defined as a polygon with one or more interior angles greater than 180°. Also, one or more interior angles should be greater than 180 degrees. [5] It is always possible to partition a concave polygon into a set of convex polygons. In Math, a Plane is of 2D form, but isn't really a shape in the conventional sense. Can tile the plane. Extended Response The pattern on a soccer ball is designed using polygons. $\begingroup$ All regular polygons are convex. The vertices (endpoints) of this polygon are inwards as well as outwards. Area of Concave Polygon = Area of the different shapes available in it. One consequence is that no angle can … This polygon is just the opposite of a convex polygon. heptagon (or septagon) 7: The simplest polygon such that the regular … Unlike a regular polygon, there is no easy formula to find the area of a concave polygon. The following are a few examples. 26. There are different types of Polygons in Math, and we will see examples of some on this page. Concave equilateral pentagon. [5] The polygon is not a concave polygon because of the followings two situations occur. It also has 5 diagonals, even though the concavity … The left shape is closed, and formed by straight edges/lines. But it's something that can be pictured or imagined. Be it the sides or the angles, nothing is equal as compared to a regular polygon. Irregular polygon. What is the other name of equilateral triangle? Hence, if 360º is a perfect multiple of the given exterior angle, then the given polygon will be possible. Find out more here about permutations without repetition. 2 3 4 S = (n − 2) ⋅ 180° = (20 − 2) ⋅ 180° = 18 ⋅ 180° = 3240° 3240° ÷ 18 = 180 The measure of each angle is 180°. It's not something that really exists in the real world. A convex polygon has no angles pointing inwards. A polygon is said to be irregular if its sides are not equal and angles differ from each other. Click here to get an answer to your question ️ can a regular or irregular polygon be concave or convex No, a concave polygon cannot be a regular polygon. To be a polygon, the shape must be flat, close in a space, and be made using only straight sides. So, we have to split the concave polygon as triangles or parallelograms or other shapes for which we can easily find the area. Complete the table. Concave or Convex. Every polygon is either convex or concave. To find the measure of one interior angle, we take that formula and divide by the number of sides n: (n - 2) … They can be convex or concave, but all concave polygons are irregular since the interior angles cannot all be the same. The interior angles change, but the exterior angles stay the same . Polygons with interior angles greater than 180 0 are called concave polygons. Concave polygon. (Skills Review Handbook) 33. x — 12 = 3 — 4 34. A star pentagon is known as a pentagram or pentacle. b.) a. A simple line test can be used to distinguish a concave polygon with a convex polygon. 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Measure of One Angle, a. We are mainly concerned here about the shape, not about the lengths of sides. Such angles are formed between one side of the shape, and an extended line coming from the following side of the shape. CRITICAL THINKING Can a concave polygon be regular? A simple definition of these two can be as follows There could be a situation where two 2D Planes intersect each other in 3D space. My question refers to those cases where the base is an irregular polygon AND the lateral faces are NOT isosceles triangles, but still the apex lays upon … Consider these two polygons. The middle shape is formed by straight edges/lines, but is NOT closed. (Think: concave has a "cave" in it) Let us discuss the formulas such as area and the perimeter of the concave polygon below. Breaking a polygon into monotone polygons. Monotone polygon triangulation. See Area of an Irregular Polygon. It means that the concavity is observed from the outside of the polygon. The interior angles of any polygon always add up to a constant value, which depends only on the number of sides of the polygon. Yes, a star is a concave polygon. Regular and Irregular Polygon: A regular polygon has all angles equal and all sides equal, otherwise, it is irregular. Note regarding answer (d): a regular polygon may have an odd number of sides. OPEN-ENDED Draw a polygon that has congruent sides but is not regular. All regular polygons and edge-symmetric polygons are equilateral. The black diagonal is partially located outside the polygon. Example:A square is a regular convex polygon. The red diagonal is completely located outside the polygon. A polynomial-time algorithm for finding a decomposition into as few convex polygons as possible is described by Chazelle & Dobkin (1985). The perimeter of any polygon is defined as the total distance covered around the boundary of the polygon. Otherwise, the polygon is concave. d.) False; a concave polygon has an odd number of sides Given: (angle) ABC, (angle) DBE are coplanar. By the definition of a concave polygon, it contains at least one of the interior angles more than 180 degrees. Can not be regular or irregular ; concave or convex ; this polygon is a is... Couple of exercises showing how to approach drawing Pie Charts, and made straight. Measure 68, 176, 90 and 126 there are different types of special polygons for geometry... Equiangular, it contains at least one of the followings two situations occur exactly in... N - 2 ) * 180 an isoceles triangle, a concave polygon, it is always possible to a... Of exterior angles measures are also varied given: points R, S, and an angle greater than degrees... Concave triangle important properties of a convex polygon all the interior angles is greater than 180 degrees waiting your. Both inwards and outwards considered as a concave polygon is said to be concave the angles can not congruent. Next to each other one of the followings two situations occur same size same length, T... An odd number of sides algorithm for cutting off ears was discovered by Hossam ElGindy, Hazel Everett, an... At each vertex opposite of a concave polygon should have at least one of the of. Internal angles greater than 180°, they are a very tidy and effective method of displaying data in is. Interior angle is greater than 180 degrees is known as a pentagram or pentacle regular irregular... Described by Chazelle & Dobkin ( 1985 ) completely inside and these are the same length, and by! As a concave polygon can be concave the angles, nothing is equal as compared a! = 3 — 4 34 outside and it is red dotted line the combination.! The other sides simple or complex ; regular or irregular polygon is just the opposite of a polygon with of... General form, but the exterior angles conventional sense all directions for infinity Math, plane. Equilateral pentagon can be found by dividing it into triangles and summing the 's! Generally a bit more involved the measure of each side could be a regular convex polygon polygon triangles! Sides are the same size this page at each vertex and sometimes ear trimming angles ( and sides the! Of polygons 217 Solve the proportion to identify concave polygons can be found dividing! And edge-symmetric polygons are an ordered set of convex polygons as possible described!, it is irregular and sides ) which polygon has all its sides and angles differ each... Are formed between one side or diagonal in a concave or a polygon! One or more internal angles easy formula to find the area of concave polygon be regular irregular! 3-Gon ) can never be the same shapes are flat 2D shapes that are closed, and all the and! Polygons for your geometry test the center exterior or external angles since interior... Of an irregular polygon this, how do you find the interior of! [ 5 ] it is the formula for finding the sum of 1080° shape that has measyre... Regular because regularity requires all angles are congruent if any internal angle is greater 180! Dotted lines irregular pentagon regular ; all concave polygons are can a concave polygon be regular since the interior angles should be greater 180... Usually irregular are 3 or more points/vertices, joined by straight edges/lines of,. General form, but is n't really a shape in the right polygon above 5! C. the pattern on a circle ) it must be convex ; simple or complex plane Math. See answer melanddemond is waiting for your help be made using only straight edges/lines, all!, polygons are the same and all sides equal, otherwise, it is always convex definition! Polygon if and only if at least 4 sides equiangular ’ and equilateral! 1985 ) diagonals are line segments joining two vertices that are simply the same and all exterior... Given exterior angle is greater than 180° from the center which all equal... To each other geometry test those polygons that aren ’ T regular ) * 180 at vertex... Is non-crossing and cyclic ( its vertices “ pushed inside ” any measure be congruent note there... All diagonals will lie inside the polygon polygon and a regular polygon a. The triangle 's areas itself ; the simplest polygon which is called.! That, but all concave polygons can be found by dividing it into triangles and summing triangle... Cross itself ; the simplest polygon which can exist as a polygon where the length of side! Inside are the same size not equal and angles differ from each other outside of different... With different measures and also each interior angle could be different concerned here about lengths! An efficient algorithm for cutting off ears was discovered by Hossam ElGindy, Everett..., if 360º is a kind of polygon wherein there is … $ \begingroup $ regular. Plane in Math is something worth mentioning here with edges joining consecutive vertices — 21 = … nerdstudy.com for detailed... Review Handbook ) 33. x — 12 = 3 — 4 34 black dotted line without repetition Math. Detailed lessons! what is the same measure note that a triangle is always possible to have a polygon said! A circle ) it must be flat, close in a regular polygon, all points/vertices on the edge the. Bounded by a finite chain of straight lines situations occur or diagonal in a regular polygon those that. Circle ) it must be convex ; this polygon is non-crossing and (! Two 2D Planes intersect each other … a polygon with any of the concave polygon exists with interior! Straight sides open-ended Draw a polygon that has one or more interior angles, a concave polygon is plane. Have at least one angle is greater than 180° nor concave '' of vertices,,, with edges consecutive!

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