Question

the measure of each interior angle of a regular polygon is 144°. 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 \( I=\frac{(n - 2)\times180^{\circ}}{n} \). We know that \( I = 144^{\circ} \), so we set up the equation \( 144=\frac{(n - 2)\times180}{n} \).

Step2: Solve the equation for \( n \)

First, multiply both sides of the equation by \( n \) to get rid of the denominator: \( 144n=(n - 2)\times180 \).
Expand the right - hand side: \( 144n = 180n-360 \).
Subtract \( 144n \) from both sides: \( 0 = 180n-144n - 360 \).
Simplify the left - hand side: \( 0 = 36n-360 \).
Add 360 to both sides: \( 36n=360 \).
Divide both sides by 36: \( n=\frac{360}{36}=10 \).

Answer:

10