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Find the interior angle on a regular polygon with 40 sides...

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User Danziger
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Given that the regular polygon with 40 sides.

We need to determine the interior angle of the polygon.

Sum of the interior angle:

Sum of the interior angle can be determined using the formula,


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

where n is the number of side.

Substituting
n=40 in the above formula, we get;


(40-2)*180^(\circ)

Simplifying the values, we get;


38*180^(\circ)=6840^(\circ)

Thus, the sum of the interior angles is 6840°

Measure of each interior angle:

The measure of each interior angle can be determined using the formula,


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

where n is the number of side.

Substituting
n=40 in the above formula, we get;


((40-2)* 180^(\circ))/(40)

Simplifying the values, we get;


(38* 180^(\circ))/(40)=(6480)/(40)

Dividing, we get,


n=171^(\circ)

Thus, the measure of each interior angle is 171°

User XCeptable
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