Question

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

Explanation:

Step1: Recall the formula for interior angle

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

Step2: Identify the number of sides

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

Step3: Substitute $n$ into the formula

Substitute $n = 8$ into $\theta=\frac{(n - 2)\times180^{\circ}}{n}$, we get $\theta=\frac{(8 - 2)\times180^{\circ}}{8}=\frac{6\times180^{\circ}}{8}=\frac{1080^{\circ}}{8}=135^{\circ}$.

Answer:

$135^{\circ}$