Calculate Interior Angles of a Regular Octagon

Published on April 12, 2026

Geometry

Learn how to find the measure of each interior angle in a regular octagon using the polygon angle sum formula. This geometry problem breaks down the steps for easy understanding.

Question

Answer

The problem asks for the measure of each interior angle in a regular octagon.

A regular octagon is a polygon with 8 equal sides and 8 equal interior angles.

The formula for the sum of the interior angles of a polygon with

sides is given by

.
For an octagon,

.
So, the sum of the interior angles of a regular octagon is

Since a regular octagon has 8 equal interior angles, the measure of each interior angle is the sum of the interior angles divided by the number of sides (or angles).
Measure of each interior angle =

To calculate

Alternatively, we can use the formula for the measure of each interior angle of a regular

-sided polygon, which is

.
For a regular octagon,

.
Measure of each interior angle =

The final answer is

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