What is the measure of an interior angle of a regular octagon?

Solution:

A regular octagon has eight equal sides and eight equal angles.

In a regular octagon, the interior angle at each vertex is 135° and the central angle is 45°.

Its interior angles add up to 1080° and the exterior angles add up to 360°.

Each exterior angle of an octagon =  360° / 8 = 45°

As interior angle and exterior angles are supplementary,  ∠i +  ∠e = 180°

∠i = 180° - 45° = 135°

Thus, in a regular octagon, the interior angle at each vertex is 135°.

What is the measure of an interior angle of a regular octagon?

Summary:

The measure of an interior angle of a regular octagon is 135°.