Question

In a regular polygon ,each interior angle is thrice the exterior angle. find the no,of sides of the polygon?

Answer 1

Hey there !

Concept : Sum of Interior angle + Sum of Exterior angle = 180°

Let the interior angle be 'x'

=> Exterior angle = 3 * Interior angle = 3 x

=> x + 3x = 180°

=> 4x = 180°

=> x = 180 / 4

=> x = 45°

We also know that,

Exterior angle = 360° / n

Where n represents the number of sides of a polygon.

=> n = 360° / Exterior angle

=> n = 360° / 45°

=> n = 8

Hence it is a 8 sided polygon which is an octagon.

Hope my answer helped !

Answer 2

Let, Write exterior angle as ext

and interior angle as int

ext = 3×int

ext + int = 180°

4×int=180°

int = 45°

So, no. of side = 180°/45° = 4

Thank you