Answer:
[tex]\begin{gathered} \text{Sum}=1260\text{ degrees} \\ m<\text{angle}=252\text{ degrees} \end{gathered}[/tex]
Step-by-step explanation:
The sum of the exterior angles of a polygon is represented by the following expression:
[tex]\begin{gathered} \text{Sum of exterior angles=(n+2)}\cdot180 \\ \text{where,} \\ n=\text{ number of vertices} \end{gathered}[/tex]
Therefore, for a pentagon:
[tex]\begin{gathered} \text{Sum}=(5+2)\cdot180 \\ \text{Sum}=7\cdot180 \\ \text{Sum}=1260\text{ degrees} \end{gathered}[/tex]
Now, divide the sum by 5 vertices, to determine the value of one of the exterior angles:
[tex]\begin{gathered} m<\text{angle}=\frac{1260}{5} \\ m<\text{angle}=252\text{ degrees} \end{gathered}[/tex]
