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

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1 Answer

3 votes

Answer:

The polygon has
12 sides.

Explanation:

Recall that the expression for finding the measure of one interior angle of a regular polygon is
(180(n-2))/(n), where
n is the number of sides the polygon has (and
n\\eq 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:


(180(n-2))/(n)=150

Solving for
n, we get:


(180(n-2))/(n)=150


(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!