Question

If an exterior angle of a regular polygon has an

angle measure of 45°, what is the measure of
each interior angle and what is the number of
sides?

Answer 1

We know that,

• Sum of the measures of all exterior angles = 360°

Measure of each exterior angle = 45°

• The number of sides of the polygon = 360°/45° = 8 .

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

As, each exterior angle is 45° ,

Therefore,

• The measure of each interior angle = 180° – 45° = 135°