Question

The measure of each angle of a regular pentagon is __________.

Answer 1

Explanation.

measure of each angle of a regular pentagon :

Sum of all the angles of a polygon $=(n-2)\times 180°$, where $n$ is the number of sides in the polygon,

Pentagon has five sides, so $n=5$

Now, sum of all angles of a pentagon is

$$\begin{gathered} =(n–2)\times 180° \\ =(5–2)\times 180° \\ =3\times 180° \\ =540° \end{gathered}$$

Measure of each angle

$$\begin{gathered} =\frac{540°}{5} \\ =108° \end{gathered}$$

Hence, the measure of each angle of a regular pentagon is $108°$.