Answer:
[tex]540^{\circ},\ 1080^{\circ},\ 1800^{\circ},\ 6840^{\circ},\ 9000^{\circ},\ 17640^{\circ}[/tex]
Step-by-step explanation:
The sum of the measures of the interior angles of each convex n-sided polygon is always equal to
[tex](n-2)\cdot 180^{\circ}.[/tex]
1. A pentagon is 5-sided polygon, then the sum of the measures of the interior angles of pentagon is
[tex](5-2)\cdot 180^{\circ}=540^{\circ}.[/tex]
2. An octagon is 8-sided polygon, then the sum of the measures of the interior angles of octagon is
[tex](8-2)\cdot 180^{\circ}=1080^{\circ}.[/tex]
3. A dodecagon is 12-sided polygon, then the sum of the measures of the interior angles of dodecagon is
[tex](12-2)\cdot 180^{\circ}=1800^{\circ}.[/tex]
4. For 40-sided polygon the sum of the measures of the interior angles is
[tex](40-2)\cdot 180^{\circ}=6840^{\circ}.[/tex]
5. For 52-sided polygon the sum of the measures of the interior angles is
[tex](52-2)\cdot 180^{\circ}=9000^{\circ}.[/tex]
6. For 100-sided polygon the sum of the measures of the interior angles is
[tex](100-2)\cdot 180^{\circ}=17640^{\circ}.[/tex]
