Question

Draw the following regular polygons. Find the sum of the angles of each of them. Find
the measure of each angle of the polygon.
(i) regul​

Answer 1

Answer:

Regular polygon

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Set of convex regular n-gons

Regular polygon 3 annotated.svgRegular polygon 4 annotated.svgRegular polygon 5 annotated.svgRegular polygon 6 annotated.svg

Regular polygon 7 annotated.svgRegular polygon 8 annotated.svgRegular polygon 9 annotated.svgRegular polygon 10 annotated.svg

Regular polygon 11 annotated.svgRegular polygon 12 annotated.svgRegular polygon 13 annotated.svgRegular polygon 14 annotated.svg

Regular polygon 15 annotated.svgRegular polygon 16 annotated.svgRegular polygon 17 annotated.svgRegular polygon 18 annotated.svg

Regular polygon 19 annotated.svgRegular polygon 20 annotated.svg

Regular polygons

Edges and vertices n

Schläfli symbol {n}

Coxeter–Dynkin diagram CDel node 1.pngCDel n.pngCDel node.png

Symmetry group Dn, order 2n

Dual polygon Self-dual

Area

(with side length, s) {\displaystyle A={\tfrac {1}{4}}ns^{2}\cot \left({\frac {\pi }{n}}\right)} {\displaystyle A={\tfrac {1}{4}}ns^{2}\cot \left({\frac {\pi }{n}}\right)}

Internal angle {\displaystyle (n-2)\times {\frac {180^{\circ }}{n}}} {\displaystyle (n-2)\times {\frac {180^{\circ }}{n}}}

Internal angle sum {\displaystyle \left(n-2\right)\times 180^{\circ }} {\displaystyle \left(n-2\right)\times 180^{\circ }}

Inscribed circle diameter {\displaystyle d_{\text{IC}}=s\cot \left({\frac {\pi }{n}}\right)} {\displaystyle d_{\text{IC}}=s\cot \left({\frac {\pi }{n}}\right)}

Circumscribed circle diameter {\displaystyle d_{\text{OC}}=s\csc \left({\frac {\pi }{n}}\right)} {\displaystyle d_{\text{OC}}=s\csc \left({\frac {\pi }{n}}\right)}

Properties Convex, cyclic, equilateral, isogonal, isotoxal

In Euclidean geometry, a regular polygon is a polygon that is equiangular (all angles are equal in measure) and equilateral (all sides have the same length). Regular polygons may be either convex or star. In the limit, a sequence of regular polygons with an increasing number of sides approximates a circle, if the perimeter or area is fixed, or a regular apeirogon (effectively a straight line), if the edge length is

Answer 2

Answer:

The sum of the exterior angles of a regular polygon is 360

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Number of sides of polygon =15

As each of the exterior angles are equal,

Exterior angle =

15

360

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=24

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