Answer
See below
Work Step by Step
(a)
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 polygon, n is 5. Compute the sum of the angles of a polygon with 5 sides as shown below:
\[\begin{align}
& \text{Sum}=\left( n-2 \right)\times 180{}^\circ \\
& =\left( 5-2 \right)\times 180{}^\circ \\
& =3\times 180{}^\circ \\
& =540{}^\circ
\end{align}\]
(b)
A measure of an angle of an irregular polygon will be determined by adding all the interior angles and subtract from the sum of the measures of all 5 angles, which is\[540{}^\circ \].
\[\begin{align}
& \text{Sum}=\text{Addition of interior angles of a polygon} \\
& =70{}^\circ +150{}^\circ +90{}^\circ +90{}^\circ +m\measuredangle A \\
& =400{}^\circ +m\measuredangle A
\end{align}\]
Compute the measurement of angle A as follows:
\[\begin{align}
& m\measuredangle A=540{}^\circ -400{}^\circ \\
& =140{}^\circ
\end{align}\]
The corresponding interior and exterior angles make a straight line, which is\[{{180}^{o}}\]. The measure of angle B that is the exterior angle of a polygon can be determined by subtracting the corresponding interior angle from \[{{180}^{o}}\].
\[\begin{align}
& m\measuredangle B=180{}^\circ -140{}^\circ \\
& =40{}^\circ
\end{align}\]
