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?

Sagot :

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

[tex]\text{Sum of angles of polygon = (n-2)180}^0[/tex]

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,

[tex]\text{Sum of angles of a pentagon=(5-2)180}^0=3\times180^0=540^0[/tex]

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

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

Hence, each interior angle is 108°