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,
[tex](n-2)\times 180^{\circ}[/tex]
where n is the number of side.
Substituting [tex]n=40[/tex] in the above formula, we get;
[tex](40-2)\times180^{\circ}[/tex]
Simplifying the values, we get;
[tex]38\times180^{\circ}=6840^{\circ}[/tex]
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,
[tex]\frac{(n-2)\times 180^{\circ}}{n}[/tex]
where n is the number of side.
Substituting [tex]n=40[/tex] in the above formula, we get;
[tex]\frac{(40-2)\times 180^{\circ}}{40}[/tex]
Simplifying the values, we get;
[tex]\frac{38\times 180^{\circ}}{40}=\frac{6480}{40}[/tex]
Dividing, we get,
[tex]n=171^{\circ}[/tex]
Thus, the measure of each interior angle is 171°
