Question

Find the sum of the measures of the interior angle of each convex polygon. show work.

Answer 1

To find the sum of the measures of the interior angle of each convex polygon:

The sum of the measures of the interior angle formula for n-gon is,

`(n-2)*180^(\circ)`

4) Given: 54 gon

`\begin{gathered} (54-2)*180^(\circ)=52*180 \\ =9360^(\circ) \end{gathered}`

5) Given: 19-gon

`\begin{gathered} (19-2)*180^(\circ)=17*180^(\circ) \\ =3060^(\circ) \end{gathered}`

6) Given: 292-gon

`\begin{gathered} (292-2)*180^(\circ)=290*180^(\circ) \\ =52200^(\circ) \end{gathered}`

7) Given: 5-gon

`\begin{gathered} (5-2)*180^(\circ)=3*180^(\circ) \\ =540^(\circ) \end{gathered}`