Question

what is the measure of one interior angle of a regular octagon?
135°
≈ 128.6°
140°
144°

Explanation:

Step1: Recall polygon - angle formula

The sum of interior angles of a polygon is given by $(n - 2)\times180^{\circ}$, where $n$ is the number of sides. For an octagon, $n = 8$. So the sum of interior angles is $(8 - 2)\times180^{\circ}=6\times180^{\circ}=1080^{\circ}$.

Step2: Find measure of one interior angle

Since a regular octagon has all interior angles equal, the measure of one interior angle is $\frac{(n - 2)\times180^{\circ}}{n}$. Substituting $n = 8$ into the formula, we get $\frac{(8 - 2)\times180^{\circ}}{8}=\frac{1080^{\circ}}{8}=135^{\circ}$.

Answer:

A. $135^{\circ}$