Question

A) By finding the size of each exterior angle of a regular polygon with 24 sides, Calculate the size of each interior angle of the polygon.
b) By finding the size of each exterior angle of a regular polygon with 36 sides, Calculate the size of each interior angle of the polygon.

I need the answer quick and I also need a step by step solution please.

Answer 1

Answer:

Let an exterior angle of a regular polygon be 'x’, then by data the interior angle is 11x

At each vertex, the adjacent angles, the exterior and interior angles are supplementary.

x+11x = 180°; so, exterior angle, x = 15° and each interior angle = 165°.

The sum of exterior angles of a polygon = 360°

Number of sides of the polygon = 360°/15° = 24 sides.

{24}-gon has 24 sides (edges), 24 vertices (corners) and 24 interior angles.

Step-by-step explanation:

The exterior and interior angles of a polygon are supplementary. Let a= interior angle, so exterior angle is 11a.

12a=180

a= 180/12 =15 degrees for the exterior angle

and interior angle = 180–15 = 165 degrees

total of the exterior angles is 360 degrees; so further 360/165 = 2.18.

Ok something is wrong here: a polygon cant have fractional sides, nor only two sides unless it is a line segment.

Answer 2

Answer:

b) By finding the size of each exterior angle of a regular polygon with 36 sides, Calculate the size of each interior angle of the polygon.