Question

the face of a watch is a regular polygon. find the measure of each interior angle of the watch face.

Explanation:

Step1: Recall polygon - angle formula

The formula for the measure of each interior angle $\theta$ of a regular polygon with $n$ sides is $\theta=\frac{(n - 2)\times180^{\circ}}{n}$. A watch - face is a dodecagon ($n = 12$).

Step2: Substitute $n = 12$ into the formula

$\theta=\frac{(12 - 2)\times180^{\circ}}{12}=\frac{10\times180^{\circ}}{12}$.

Step3: Calculate the value

$\frac{10\times180^{\circ}}{12}=150^{\circ}$.

Answer:

$150^{\circ}$