Question

for a regular 15 - gon, find the measure of one interior angle.

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 15 - gon, \( n = 15 \).

Step2: Calculate the sum of interior angles

Substitute \( n = 15 \) into the formula: \( S=(15 - 2)\times180^{\circ}=13\times180^{\circ} = 2340^{\circ} \).

Step3: Find the measure of one interior angle

In a regular polygon, all interior angles are equal. So the measure of one interior angle \( I=\frac{S}{n} \). Substitute \( S = 2340^{\circ} \) and \( n = 15 \): \( I=\frac{2340^{\circ}}{15}=156^{\circ} \).

Answer:

\( 156^{\circ} \)