Answer
See below
Work Step by Step
(a)
Sum of the measures of the angles will be determined by using the formula\[\left( n-2 \right)180{}^\circ \]. The sides of the polygon, n is 4. Compute the sum of the angles of a polygon with 4 sides as shown below:
\[\begin{align}
& \text{Sum}=\left( n-2 \right)\times 180{}^\circ \\
& =\left( 4-2 \right)\times 180{}^\circ \\
& =2\times 180{}^\circ \\
& =360{}^\circ
\end{align}\]
(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 4 angles, which is\[360{}^\circ \].
Sum of interior angles of a polygon can be done as mentioned below:
\[\begin{align}
& \text{Sum}=\text{Total of Interior angles } \\
& =42{}^\circ +90{}^\circ +90{}^\circ +m\measuredangle A \\
& =222{}^\circ +m\measuredangle A
\end{align}\]
Compute the measurement of angle A as shown below:
\[\begin{align}
& m\measuredangle A={{360}^{0}}-222{}^\circ \\
& ={{138}^{o}}
\end{align}\]
The corresponding interior and exterior angles make a straight line, which is\[180{}^\circ \]. The measure of angle B that is the exterior angle of a polygon can be determined by subtracting the corresponding interior angle from \[{{180}^{o}}\].
\[\begin{align}
& m\measuredangle B=180{}^\circ -138{}^\circ \\
& =42{}^\circ
\end{align}\]
