Question

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

Explanation:

Step1: Identify number of sides

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

Step2: Calculate total interior angles

Use formula for total interior angles:
$$(n-2)\times180^\circ$$
$$(8-2)\times180^\circ=6\times180^\circ=1080^\circ$$

Step3: Find each interior angle

Divide total by number of sides:
$$\frac{1080^\circ}{8}=135.0^\circ$$

Answer:

$135.0^\circ$