Question

the measure of each interior angle of a regular polygon is 108°. find the number of sides.
number of sides =

Explanation:

Step1: Recall the formula for interior angle of a regular polygon

The formula for the measure of each interior angle \( I \) of a regular polygon with \( n \) sides is \( I=\frac{(n - 2)\times180^{\circ}}{n} \), where \( n \) is the number of sides.

Step2: Substitute the given interior angle and solve for \( n \)

We know that \( I = 108^{\circ} \), so we substitute into the formula:

$$ 108=\frac{(n - 2)\times180}{n} $$

Multiply both sides by \( n \) to get rid of the denominator:

$$ 108n=(n - 2)\times180 $$

Expand the right - hand side:

$$ 108n = 180n-360 $$

Subtract \( 108n \) from both sides:

$$ 0=180n - 108n-360 $$

$$ 0 = 72n-360 $$

Add 360 to both sides:

$$ 72n=360 $$

Divide both sides by 72:

$$ n=\frac{360}{72}=5 $$

Answer:

5