Question

regular polygon, the measure of each interior angle is 150°. how many sides does polygon have? the polygon has □ sides. question 5, 11.3.a-10 hw score: 30.77%, 4 of 13 points points: 0 of 1

Explanation:

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

The formula for the measure of each interior angle of a regular polygon with \( n \) sides is \( I=\frac{(n - 2)\times180^{\circ}}{n} \), where \( I \) is the measure of each interior angle. We know that \( I = 150^{\circ} \), so we set up the equation:
\[
150=\frac{(n - 2)\times180}{n}
\]

Step2: Solve the equation for \( n \)

First, multiply both sides of the equation by \( n \) to get rid of the denominator:
\[
150n=(n - 2)\times180
\]
Expand the right - hand side:
\[
150n = 180n-360
\]
Subtract \( 150n \) from both sides:
\[
0=180n - 150n-360
\]
Simplify the right - hand side:
\[
0 = 30n-360
\]
Add 360 to both sides:
\[
30n=360
\]
Divide both sides by 30:
\[
n=\frac{360}{30}=12
\]

Answer:

12