Answer
The measure of an angle 1 in a 5-sided polygon is\[65{}^\circ \].
Work Step by Step
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. 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:
\[\begin{align}
& \text{Sum of angles}=\left( n-2 \right)\times 180{}^\circ \\
& =\left( 5-2 \right)\times 180{}^\circ \\
& =3\times 180{}^\circ \\
& =540{}^\circ
\end{align}\]
Sum of interior angles of a polygon. The corresponding interior and exterior angles make a straight line, which is\[{{180}^{o}}\]. Compute the sum of interior angles as follows:
\[\begin{align}
& \text{sum of angles}=140{}^\circ +135{}^\circ +\left( 180{}^\circ -97{}^\circ \right)+\left( 180{}^\circ -63{}^\circ \right) \\
& =140{}^\circ +135{}^\circ +83{}^\circ +117{}^\circ \\
& =475{}^\circ
\end{align}\]
Compute the measurement of angle 1 as follows:
\[\begin{align}
& m\measuredangle 1=540{}^\circ -475{}^\circ \\
& =65{}^\circ
\end{align}\]
