Question

In a regular polygon, each interior angle is thrice the exterior angle. The number of sides of the polygon is

(a) 6 (b) 8 (c) 10 (d) 12

Answer 1

Let $x$ be the exterior angle

Interior Angle $=3x$

Interior Ange $+$ Exterior Angle $={180}^{\circ }$

$x=\frac{180}{4}$

So, Exterior Angle $={45}^{\circ }$

Number of sides $=\frac{360}{45}$

$=8$

Hence, the number of sides of the polygon is $8$.

Option (b) is correct.