Question

find a measure of the angle sum each interior angle and each exterior angle for the polygon round your answer to the nearest tenth if necessary

Answer 1

To calculate the sum of the interior angles of an polygon we have to use the following formula:

`S=(n-2)\cdot180`

Where n is the number of sides of the polygon. So we have that for the first one is

`S=(7-2)\cdot180=5\cdot180=900^(\circ)`

for the second one:

`S=(10-2)\cdot180=8\cdot180=1440^(\circ)`

To know the interior angles of a polygon we have to use the following formula:

`\alpha=180-(360)/(n)`

where n is number of sides of the polygon. So we get

`\alpha=180-(360)/(7)\approx128.57^(\circ)`

For the second one:

`\alpha=180-(360)/(10)=144^(\circ)`