In general, the sum of the inner angles of an n-sided polygon is given by the formula below
[tex]\begin{gathered} sum\text{ of inner angles}=(n-2)*180\degree \\ n\rightarrow\text{ number of sides of the polygon} \end{gathered}[/tex]
12) In the case of a 5-sided polygon,
[tex]\begin{gathered} (n-2)*180=3*180=540 \\ \Rightarrow5x+5x+7x+8x+7x=540 \\ \Rightarrow32x=540 \\ \Rightarrow x=16.875 \\ \Rightarrow x\approx16.88 \end{gathered}[/tex]
Once rounded, the answer to question 12) is x=16.88.
13) The polygon has 6 sides; then,
[tex]\begin{gathered} (6-2)*180=720 \\ \Rightarrow5x+4x+2x+7x+x+4x=720 \\ \Rightarrow23x=720 \\ \Rightarrow x=\frac{720}{23} \\ \Rightarrow x\approx31.30 \end{gathered}[/tex]
The exact answer to question 13) is x=720/23, rounded to 2 decimal places the answer is 13.30
