Question

1, Find the interior angle of a regular polygon with 20 sides. What is the size of exterior angle?

2, Calculate the
(I) exterior angle
(ii) the number of sides of a regular polygon with an interior angle of
(a) 60° (b) 72° (c) 165°​

Answer 1

Explanation:

1) (20 -2) * 180 = 3240 (sum of the inner angles)

3240 : 20 = 162 degrees

2) (I) 180 - 162 = 18 degrees

(ii)

a = 3 (it is an equilateral triangle)

b = 5 (it is a pentagon)

c = 24

Answer 2

1. 180(n-2) gives you the angle sum

devide by n to get the value of one interior angle

n are the number of sides, or corners

180(20-2)/20 = 162° is the interior angle.

the exterior angle is just 360°-162° = 198°

2i) seems to be included in 1), pls clarify if that's not the case.

remember

180(n-2)/n = int.angle

let's do this with (a) 60°

180(n-2)/n = 60

(180n-360)/n = 60 |*n

180n-360 = 60n |-180n

-360 = -120n |/(-120)

3 = n

2iia) 3 sides / triangle

2iib) 5 sides / pentagon

2iic) 24 sides