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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

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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)

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