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

The measure of one interior angle of a regular octagon is

135^\circ

To find a single interior angle of a regular polygon, use the formula

\frac{(n - 2) \times 180^\circ}{n}

. Substituting

n = 8

for an octagon gives

\frac{6 \times 180^\circ}{8} = \frac{1080^\circ}{8} = 135^\circ

Identify the number of sides (

n

) for an octagon.

n = 8

An octagon is a polygon with 8 sides.

Calculate the total sum of the interior angles using the formula

(n - 2) \times 180^\circ

(8 - 2) \times 180^\circ = 6 \times 180^\circ = 1080^\circ

This formula determines the combined measure of all interior angles for any polygon.

Divide the total sum by the number of sides to find the measure of a single angle.

1080^\circ \div 8 = 135^\circ

In a regular polygon, all interior angles are equal, so dividing the total sum by the number of angles gives the measure of one.

Interior Angles of Regular Polygons

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