Question

find the measure of each interior angle of a regular octagon. if needed, round to the nearest tenth.

Explanation:

Step1: Recall the formula for the sum of interior angles of a polygon.

The formula for the sum of the interior angles of a polygon with \( n \) sides is \( S=(n - 2)\times180^{\circ} \). For a regular octagon, the number of sides \( n = 8 \).

Step2: Calculate the sum of interior angles.

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

Step3: Find the measure of each interior angle.

In a regular polygon, all interior angles are equal. So, to find the measure of each interior angle, we divide the sum of the interior angles by the number of sides \( n \). That is, each interior angle \( A=\frac{S}{n} \). Substituting \( S = 1080^{\circ} \) and \( n = 8 \), we get \( A=\frac{1080^{\circ}}{8}=135^{\circ} \).

Answer:

\( 135^{\circ} \)