Question

find the measure of each interior angle of the regular polygon. the measure of each interior angle is square^{circ}.

Explanation:

Step1: Determine the number of sides \(n\)

The polygon is a regular 12 - sided polygon (\(n = 12\)).

Step2: Use the formula for the measure of an interior angle of a regular polygon

The formula for the measure of an interior angle \(\theta\) of a regular polygon is \(\theta=\frac{(n - 2)\times180^{\circ}}{n}\).
Substitute \(n = 12\) into the formula: \(\theta=\frac{(12 - 2)\times180^{\circ}}{12}\).
First, calculate \(12-2=10\). Then, \((10\times180^{\circ}) = 1800^{\circ}\).
Finally, \(\frac{1800^{\circ}}{12}=150^{\circ}\).

Answer:

\(150^{\circ}\)