Chapter 12, Problem 12MCQ

To determine

To find: The measure of an interior angle of a regular pentagon.

Answer to Problem 12MCQ

The value of an interior angle of a regular pentagon is ${108}^{\circ }$ .

Explanation of Solution

Given information: A regular pentagon.

Calculation: A regular pentagon is a five-sided polygon.

The sum of the interior angles of a polygon $=(\text{n}-2)\times {180}^{\circ }$

Where, for the pentagon, $\text{n}=5$

The sum of the interior angles of the pentagon is,

  $\begin{array}{l}=(\text{n}-2)\times {180}^{\circ }\\ =(5-2)\times {180}^{\circ }\\ =3\times {180}^{\circ }\\ ={540}^{\circ }\end{array}$

The number of angle of the pentagon is $5$ .

Let’s find an interior of the regular pentagon,

  $\begin{array}{l}=\frac{{540}^{\circ }}{5}\\ ={108}^{\circ }\end{array}$

Hence, The value of an interior angle of a regular pentagon is ${108}^{\circ }$ .