Question

The Pentagon building in Washington, D.C., is named because it is in the shape ofa regular pentagon. What is the measure of each interior angle?

Answer 1

The formula to find the sum of the interior angles of a polygon is given below,

`\text{Sum of angles of polygon = (n-2)180}^0`

Number, n, of sides of a regular pentagon is 5 i.e n = 5,

To find the sum of angles in a regular pentagon, substitute for n into the formula above,

`\text{Sum of angles of a pentagon=(5-2)180}^0=3*180^0=540^0`

To find the measure of each angle of the pentagon, the formula is given below

`\begin{gathered} for\text{ each interior angle=}\frac{Sum\text{ of angles}}{n} \\ \text{Where n = 5} \\ \text{For each interior angle=}(540^0)/(5)=108^0 \end{gathered}`

Hence, each interior angle is 108°