Answer
Regular pentagon is a closed polygon with five sides and all angles are of same degree measure.
Work Step by Step
A regular polygon is a closed figure with all its sides of the same length. Also, the angles are of same degree measure in a regular polygon.
The sum of the measures of the angles will be determined by using the formula\[\left( n-2 \right)\times 180{}^\circ \]. The sides of the pentagon, n is 5. Compute the sum of the angles of a pentagon with 5 sides as shown below:
\[\begin{align}
& \text{Sum of angles}=\left( n-2 \right)\times 180{}^\circ \\
& =\left( 5-2 \right)\times 180{}^\circ \\
& =3\times 180{}^\circ \\
& =540{}^\circ
\end{align}\]
A measure of an angle of a regular pentagon will be determined by dividing the sum of the measures of all 5 angles by its sides, i.e., 5.
\[\begin{align}
& m\measuredangle A=\frac{540{}^\circ }{5} \\
& ={{108}^{o}}
\end{align}\]
