Answer
The measure of each angle of a 5-sided polygon represented by x is\[108{}^\circ \].
Work Step by Step
Sum of the measures of the angles will be determined by using the formula\[\left( n-2 \right)\times 180\]. The sides of the polygon, n is 5. Compute the sum of the angles of a polygon with 5 sides as shown below:
\[\begin{align}
& \text{Sum of angles}=\left( n-2 \right)\times 180{}^\circ \\
& =\left( 5-2 \right)\times 180{}^\circ \\
& =3\times 180{}^\circ \\
& =540{}^\circ
\end{align}\]
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\[{{540}^{o}}\].
\[\begin{align}
& \text{Measure of each angle of a polygon}=108{}^\circ +6x-12{}^\circ +5x+8{}^\circ +4x+28{}^\circ +3x+48{}^\circ \\
& {{540}^{o}}={{180}^{o}}+18x \\
& x=\frac{540{}^\circ -180{}^\circ }{18} \\
& =\frac{360{}^\circ }{18}
\end{align}\]
\[=20{}^\circ \]
Compute the other angles by substituting the values of x as mentioned below:
First angle:
\[\begin{align}
& \text{Measure of angle}=6x-12{}^\circ \\
& =\left( 6\times 20{}^\circ \right)-12{}^\circ \\
& =108{}^\circ
\end{align}\]
Second angle:
\[\begin{align}
& \text{Measure of angle}=5x+8{}^\circ \\
& =\left( 5\times 20{}^\circ \right)+8{}^\circ \\
& =108{}^\circ
\end{align}\]
Third angle:
\[\begin{align}
& \text{Measure of angle}=4x+28{}^\circ \\
& =\left( 4\times 20{}^\circ \right)+28{}^\circ \\
& =108{}^\circ
\end{align}\]
Fourth angle:
\[\begin{align}
& \text{Measure of angle}=3x+48{}^\circ \\
& =\left( 3\times 20{}^\circ \right)+48{}^\circ \\
& =108{}^\circ
\end{align}\]
