Question

30 what is the measure of each interior angle in a regular octagon?

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 interior angles by the number of sides. That is, \( \text{Each interior angle}=\frac{S}{n}=\frac{1080^{\circ}}{8} = 135^{\circ} \).

Answer:

\( 135^{\circ} \)