Answer
Measure of angle A is\[120{}^\circ \] and a measure of angle B is\[60{}^\circ \].
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. Total measure of the angles will be determined by using the formula, \[\left( n-2 \right)\times 180{}^\circ \].
The sides of the polygon, n is 6. Compute the sum of the angles of a polygon with 6 sides as shown below:
\[\begin{align}
& \text{Sum}=\left( n-2 \right)\times 180{}^\circ \\
& =\left( 6-2 \right)\times 180{}^\circ \\
& =4\times 180{}^\circ \\
& ={{720}^{o}}
\end{align}\]
A measure of an angle of a regular polygon will be determined by dividing the sum of the measures of all angles, which is\[720{}^\circ \] by its sides, i.e., 6.
\[\begin{align}
& m\measuredangle A=\frac{720{}^\circ }{6} \\
& =120{}^\circ
\end{align}\]
The measure of angle B that is the 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.
\[\begin{align}
& m\measuredangle B=\frac{360{}^\circ }{6} \\
& =60{}^\circ
\end{align}\]
Hence,the measure of the angle A of a regular polygon is\[120{}^\circ \] and the measure of the angle B of a regular polygon is\[60{}^\circ \].
