Question

What is the sun of the exterior angles and what is the value of one of the exterior angles

Answer 1

`\begin{gathered} \text{Sum}=1260\text{ degrees} \\ m<\text{angle}=252\text{ degrees} \end{gathered}`

Explanation:

The sum of the exterior angles of a polygon is represented by the following expression:

`\begin{gathered} \text{Sum of exterior angles=(n+2)}\cdot180 \\ \text{where,} \\ n=\text{ number of vertices} \end{gathered}`

Therefore, for a pentagon:

`\begin{gathered} \text{Sum}=(5+2)\cdot180 \\ \text{Sum}=7\cdot180 \\ \text{Sum}=1260\text{ degrees} \end{gathered}`

Now, divide the sum by 5 vertices, to determine the value of one of the exterior angles:

`\begin{gathered} m<\text{angle}=(1260)/(5) \\ m<\text{angle}=252\text{ degrees} \end{gathered}`