Answer
.Measure of two angles represented by x is\[115{}^\circ \]each and others two is\[120{}^\circ \]each respectively.
Work Step by Step
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 6. Compute the sum of the angles of a polygon with 6 sides as shown below:
\[\begin{align}
& \text{sum}=\left( n-2 \right)\times 180{}^\circ \\
& =\left( 6-2 \right)\times 180{}^\circ \\
& =4\times 180{}^\circ \\
& =720{}^\circ
\end{align}\]
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 6 angles, which is\[{{720}^{o}}\]. Compute the measurement as follows:
\[\begin{align}
& \text{Measure of each angle of a polygon}=130{}^\circ +120{}^\circ +x+x+x+5{}^\circ +x+5{}^\circ \\
& 720{}^\circ =260{}^\circ +4x \\
& x=\frac{720{}^\circ -260{}^\circ }{4} \\
& =\frac{460{}^\circ }{4} \\
& =115{}^\circ
\end{align}\]
Compute the measurement of another angle as follows:
\[\begin{align}
& \text{other angle measurement}=x+5{}^\circ \\
& =115{}^\circ +5{}^\circ \\
& =120{}^\circ
\end{align}\]
