Question

Find the measure of an interior angles of a regular 12-gon.

Short answer

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

Step-by-step solution

Step 1. Given Information.

The polygon is regular 12-gon.

Step 2. Formula used.

The sum of the measure of the all-interior angles of a convex n-gon is $\left(n-2\right)\times 180°$.

Step 3. Calculation.

Here, polygon is 12-gon that is $n=12$.

Calculate the sum of the all-interior angle of a regular 12-gon.

$\begin{array}{c}\left(n-2\right)\times 180°=\left(12-2\right)\times 180°\\ =10\times 180°\\ =1800°\end{array}$

Evaluate the size of 1 angle by dividing the sum by the total number of sides that is 12.

$\begin{array}{c}\text{Angle}=\frac{1800°}{12}\\ =150°\end{array}$

Step 4. Conclusion.

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