Question

In a regular polygon, each interior angle is thrice the exterior angle. The number of sides of
(a)6
(b)8
(c) 10
(d) 12​

Answer 1

answer is 8

Step-by-step explanation:

Interior angle = 3a

We know that,

Exterior angle + Interior angle = 180

=> a + 3a = 180

=> 4a = 180

=> a = 45°

Interior angle = 3 × 45 = 135°

Exterior angle = 45°

Now,

n × Each Exterior angle = 360

=> n × 45 = 360

=> n = 8

Number of sides = 8