Question

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

Answer 1

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,

$(n-2)\times 180^{\circ}$

where n is the number of side.

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

$(40-2)\times180^{\circ}$

Simplifying the values, we get;

$38\times180^{\circ}=6840^{\circ}$

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,

$\frac{(n-2)\times 180^{\circ}}{n}$

where n is the number of side.

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

$\frac{(40-2)\times 180^{\circ}}{40}$

Simplifying the values, we get;

$\frac{38\times 180^{\circ}}{40}=\frac{6480}{40}$

Dividing, we get,

$n=171^{\circ}$

Thus, the measure of each interior angle is 171°