Answer
Measure of angle A is\[108{}^\circ \]and of angle B is\[72{}^\circ \].
Work Step by Step
Regular polygon is a closed figure with all of its sides of same length. Also, the angles are of same degree measure in regular polygon. Total measures of the angles will be determined by using the formula, \[\left( n-2 \right)\times 180{}^\circ \]. The sides of the polygon, n is 5.
Compute the sum of the angles of polygon with 5 sides as shown below:
\[\begin{align}
& \text{Sum}=\left( n-2 \right)\times 180{}^\circ \\
& =\left( 5-2 \right)\times 180{}^\circ \\
& =3\times 180{}^\circ \\
& =540{}^\circ
\end{align}\]
Measure of an angle of a regular polygon will be determined by dividing the sum of the measures of all angles, which is \[540{}^\circ \]by its sides, i.e.,5.
\[\begin{align}
& m\measuredangle A=\frac{540{}^\circ }{5} \\
& =108{}^\circ
\end{align}\]
The measure of angle B that is exterior angle of a regular polygon can be determined by dividing the sum of the measures of exterior angles of a regular polygon that is\[360{}^\circ \] by the number of sides, n.
\[\begin{align}
& m\measuredangle B=\frac{360{}^\circ }{5} \\
& =72{}^\circ
\end{align}\]
Hence, the measure of the angle A of a regular polygon is\[108{}^\circ \]. The measure of the angle B of a regular polygon is\[72{}^\circ \].
