How many sides does a polygon with an interior angle measure of 120 degrees have? Show your work.?

Question

How many sides does a polygon with an interior angle measure of 120 degrees have? Show your work.

Answer 1

Hey there!

Let's use the formula N=180(n-2)/n, where N is the measure of interior angle and n is the number of sides.

N=180(n-2)/n --> Write the problem.
120=180(n-2)/n --> Substitute 120 for n.
120n=180(n-2) --> Multiply n on both sides of the equation.
120n=180n-360 --> Distribute 180 into n-2.
-60n=-360 --> Subtract 180n on both sides of the equation.
n=6 Divide -60 on both sides of the equation.

So the polygon has 6 sides.

Hope it helps!

Answer 2

There is not enough information given. For example, consider a triangle with angles 30, 30, and 120. Or a quadrilateral with interior angles 80, 80, 80, and 120.

In general, consider a polygon with n (>= 3) sides, with one interior angle 120, and n - 1 remaining angles all equal. Each of these is "a polygon with an interior angle" of 120 degrees.