How many sides does a regular polygon have if each of its interior angles is 165 degree?Grade : 9

# How many sides does a regular polygon have if each of its interior angles is 165 degree?Grade : 9

1. A
A.25
2. B
B.24
3. C
C.23
4. D
D.22

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### Solution:

Given that ,
Interior angle, x=165°
Therefore , exterior angle = (180-x)
=(180°−165°)=15°
We know that the sum of all exterior angles of any polygon is 360 degree.
Therefore number of sides
=360° ÷ each exterior angle
=360° ÷ 15°
= 24
So, the number of sides a regular polygon has if its interior angle is 165° are 24.

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