We are asked to find the measure of each interior angle in a regular polygon with 8 sides (an octagon).

1. Problem Description

We are asked to find the measure of each interior angle in a regular polygon with 8 sides (an octagon).

2. Solution Steps

First, we need to find the sum of the interior angles of an octagon. The formula for the sum of the interior angles of a polygon with $n$ sides is given by:

$S = (n-2) \times 180^{\circ}$

In this case, $n = 8$, so we have:

$S = (8-2) \times 180^{\circ} = 6 \times 180^{\circ} = 1080^{\circ}$

Since the polygon is regular, all its interior angles are equal. To find the measure of each interior angle, we divide the sum of the interior angles by the number of sides, which is

8.

Each interior angle $= \frac{1080^{\circ}}{8} = 135^{\circ}$

3. Final Answer

135