Question

Find the measure of the sum of the angles of a pentagon.

Answer 1

$ABCDE$ is the required pentagon.

We know that the interior angle of a polygon is given by

$(n-2)\times {180}^0$, where $n=$number of sides

A pentagon has $5$ sides. Thus $n=5$.

So, the sum of the angles of a pentagon

$$\begin{gathered} =(n-2)\times {180}^0 \\ =(5-2)\times {180}^0 \\ =3\times {180}^0 \\ ={540}^0 \end{gathered}$$.

Therefore, the sum of the angles of a pentagon is $540°$.