POLYGONS 1

An interior angle of a regular polygon is three as much as an exterior angle. Find the interior angle.

Solution

Let i = interior angle, e = exterior angle.

Now i  + e=180⁰…………………(1)

But i = 3e…………………(2)

Substitute (2) in (1) above.

i  + e=180⁰

3e   + e=180⁰

4e =180⁰

4e=180⁰          dividing by 4 both sides.

4      4

e = 45⁰

But from equation (2)

But i = 3e

      i = 3 x 45⁰

      i = 135⁰

Hence interior angle is 135⁰

TRY THIS………………………   

An interior angle of a regular polygon is two as much as an exterior angle. Find the interior angle.