Question

what is the measure of one interior angle of the regular octagon shown below?
a. 108°
b. 120°
c. 135°
d. 144°

Explanation:

Step1: Recall sum - of - interior - angles 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 $S=(8 - 2)\times180^{\circ}=6\times180^{\circ}=1080^{\circ}$.

Step2: Calculate one interior angle

Since a regular octagon has all interior angles equal, one interior angle $\theta=\frac{S}{n}$.
Substituting $S = 1080^{\circ}$ and $n = 8$, we get $\theta=\frac{1080^{\circ}}{8}=135^{\circ}$.

Answer:

C. $135^{\circ}$