Question

what is the measure of each angle in a regular polygon with 8 sides?

Explanation:

Step1: Calculate sum of interior angles

The formula for the sum of interior angles of an n-sided polygon is $(n-2)\times180^\circ$. For $n=8$:
$$(8-2)\times180^\circ = 6\times180^\circ = 1080^\circ$$

Step2: Divide by number of angles

A regular polygon has equal angles, so divide the total sum by 8:
$$\frac{1080^\circ}{8} = 135^\circ$$

Answer:

$135^\circ$