Question

the measure of an interior angle of a regular polygon is $144^{circ}$. find the number of sides in the polygon.
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Explanation:

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

The formula for the measure of an interior angle of a regular polygon with \( n \) sides is \( \frac{(n - 2)\times180^{\circ}}{n} \). We know the interior angle is \( 144^{\circ} \), so we set up the equation \( \frac{(n - 2)\times180}{n}=144 \).

Step2: Solve the equation for \( n \)

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

Answer:

10