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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
For an octagon,
So, the sum of the interior angles of a regular octagon is
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 =
Measure of each interior angle =
To calculate
Alternatively, we can use the formula for the measure of each interior angle of a regular
For a regular octagon,
Measure of each interior angle =
For a regular octagon,
Measure of each interior angle =
The final answer is