Question

Find the measure of each angle 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 $\left(\frac{360°}{n}\right)=\left(\frac{360°}{8}\right)=45°$.

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 $135°$.