Question

Find the measure of each angle in degrees of a regular octagon.

Answer 1

Step 1: Find the value of each exterior angle:

The given geometry is a regular octagon.

Thus, the number of sides, $n=8$.

It is known that the sum of all exterior angles of a polygon is $360°$.

As the given octagon is regular, so the value of each exterior angle can be given by

Step 2: Find the value of each interior angle:

It is known that the sum of an interior angle and the corresponding exterior angle is $180°$.

Thus, the value of each interior angle of the regular octagon can be given by, $\left(180°-45°\right)=135°$.

Hence, the measure of each angle of a regular octagon is $\mathbf{135}\mathbf{°}$.