Question

Find the number of sides of a regular polygon whose each interior angle is of 135?

Answer 1

Hey

Here is your answer,

The sum of the exterior angles of a polygon is 360°.

For regular polygons the exterior angles are the same (congruent).

Interior + exterior = 180°

135° + exterior = 180°

exterior = 45°

360°/45°
= 8 sides.

Hope it helps you!

Answer 2

Given:

Interior Angle of a regular polygon is 135°

To Find:

The number of sides of the regular polygon.

Solution:

We know that,

For regular polygons the exterior angles are the same (congruent).

So,

The sum of interior and exterior angle is 180°

⇒ interior angle + exterior angle = 180°

                   135° + exterior angle = 180°

                           ∴exterior angle = 180° - 135°  = 45°

In order to find the number of sides, we calculate

360°/45° = 8

Hence, there are 8 sides to a regular polygon whose each interior angle is of 135°.