Question

The measure of each Interior angle of a regular polygon is 135º. Find the number of sides.

Number of sides
5
?​

Answer 1

The number of sides of the polygon with 135° interior angle is 8

Explanation:

Given as :

The measure of each interior angle of regular polygon = 135°

Let The total number of sides = n

So, each internal angle of a regular polygon with n sides =
`180^(\circ)- (360^(\circ))/(n)`

or, 135° =
`180^(\circ)- (360^(\circ))/(n)`

or,
`(360^(\circ))/(n)` = 180° - 135°

or,
`(360^(\circ))/(n)` = 45°

∴ n =
`(360^(\circ))/(45^(\circ))`

I.e n = 8

Hence the number of sides of the polygon with 135° interior angle is 8 Answer