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 = nThen 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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