# 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°.

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