Question

There are 2 questions I need help with. I uploaded a picture

Answer 1

In general, the sum of the inner angles of an n-sided polygon is given by the formula below

`\begin{gathered} sum\text{ of inner angles}=(n-2)*180\degree \\ n\rightarrow\text{ number of sides of the polygon} \end{gathered}`

12) In the case of a 5-sided polygon,

`\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}`

Once rounded, the answer to question 12) is x=16.88.

13) The polygon has 6 sides; then,

`\begin{gathered} (6-2)*180=720 \\ \Rightarrow5x+4x+2x+7x+x+4x=720 \\ \Rightarrow23x=720 \\ \Rightarrow x=(720)/(23) \\ \Rightarrow x\approx31.30 \end{gathered}`

The exact answer to question 13) is x=720/23, rounded to 2 decimal places the answer is 13.30