Yoshika Tripathi
Yoshika Tripathi
6 years ago

How many sides in a regular polygon has, if each of it's interior angle is 135°

A. 8

B. 7

C. 6

D. 10

Answer: Option A

Solution(By Examveda Team)

Let the number of sides of a regular polygon = n
Then the measure of each of its interior angle = [(2n – 4) × 90°]/n
Given measure of each angle = 135°
Therefore, [(2n – 4) × 90]/n = 135
⇒ (2n – 4) × 90 = 135n
⇒ 180n – 360 = 135n
⇒ 180n - 135n = 360
⇒ 45n = 360
⇒ n = 360/45
⇒ n = 8
Therefore the number of sides of the regular polygon is 8

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