Question

the measure of each interior angle of a regular polygon is 156°. find the number of sides.
number of sides =

Explanation:

Step1: Recall the formula for interior angle

The formula for the measure of each interior angle \( I \) of a regular polygon with \( n \) sides is \( I=\frac{(n - 2)\times180^{\circ}}{n} \). We know \( I = 156^{\circ} \), so we set up the equation \( 156=\frac{(n - 2)\times180}{n} \).

Step2: Solve the equation for \( n \)

Multiply both sides by \( n \): \( 156n=(n - 2)\times180 \).
Expand the right side: \( 156n = 180n-360 \).
Subtract \( 156n \) from both sides: \( 0 = 24n-360 \).
Add 360 to both sides: \( 24n = 360 \).
Divide both sides by 24: \( n=\frac{360}{24}=15 \).

Answer:

15