Chapter 12.3, Problem 2C

To determine

To find:the measure of an interior angle of a regular 12-gon.

Answer to Problem 2C

The measure of an interior angle of a regular 12-gonis $150°$

Explanation of Solution

Given information:

Formula Used:

Sum $=\left(n-2\right)\cdot 180°$

Sum = $\frac{\text{sum}}{\text{n}}$

Calculation:

Substitute the value of n

  $\begin{array}{l}\text{sum}=\left(12-2\right)\cdot 180°\\ =10\cdot 180°\\ =1800°\end{array}$

Evaluate the size of 1 angle by dividing the sum with the total number of side

Therefore the angles of polygon is

  $\begin{array}{l}\text{angle}=\frac{\text{sum}}{\text{n}}\\ =\frac{1800°}{12}\\ =150°\end{array}$

Hence, the measure of an interior angle of a regular 12-gonis $150°$