what is the measure of each interior angle of the regular polygon pictured below? if necessary, round to the…

Explanation:

Step1: Recall the formula

The formula for the measure of each interior angle $\theta$ of a regular polygon is $\theta=\frac{(n - 2)\times180^{\circ}}{n}$, where $n$ is the number of sides of the polygon.

Step2: Identify the number of sides

The pictured polygon is an octagon, so $n = 8$.

Step3: Calculate the interior - angle measure

Substitute $n = 8$ into the formula: $\theta=\frac{(8 - 2)\times180^{\circ}}{8}=\frac{6\times180^{\circ}}{8}=\frac{1080^{\circ}}{8}=135^{\circ}$.

Answer:

$135^{\circ}$