Question

the measure of an interior angel of a regular polygon is 150. find the number of sides in the polygon.

Answer 1

Answer:

The polygon has $12$ sides.

Step-by-step explanation:

Recall that the expression for finding the measure of one interior angle of a regular polygon is $\frac{180(n-2)}{n}$, where $n$ is the number of sides the polygon has (and $n\neq 0$), which is what we want to find.

Because the measure of one interior angle of the given polygon is $150\textdegree$, we can write the following equation to solve for $n$:

$\frac{180(n-2)}{n}=150$

Solving for $n$, we get:

$\frac{180(n-2)}{n}=150$

$\frac{180n-360}{n}=150$ (Distribute the $180$ in the numerator)

$180n-360=150n$ (Multiply both sides of the equation by $n$ to eliminate the denominator and simplify)

$30n-360=0$ (Subtract $150n$ from both sides of the equation and simplify)

$30n=360$ (Add $360$ to both sides of the equation to isolate $n$ and simplify)

$\bf n=12$ (Divide both sides of the equation by $30$ to get rid of $n$'s coefficient and simplify)

Therefore, the polygon has $\bf 12$ sides. Hope this helps!