ACT Math: A Challenging Polygons Problem

We’ve listed this problem under “ACT Math,” but you could just as easily see a problem like this on the SAT Math test as well. Give the problem a try, and then scroll down for the solution.

A regular polygon is covered by a piece of paper so that only one of its interior angles is visible. You are able to determine that the interior angle is four times as large as the exterior angle. How many sides does the polygon have?

A.  8

B.  9
C.  10
D.  11
E.  12


(Scroll down for the solution)
The interior angle and the exterior angle form a linear pair and the sum of their angle measures is 180 degrees. You can write and solve an equation to find the value of x:

4x + x = 180
5x = 180
x = 36

You now know that the interior angle is 4 x 36 = 144 degrees and the exterior angle is 36 degrees. You could work with the interior angles formula, but it’s much easier if you remember that the exterior angles of any polygon always sum to 360 degrees. Dividing 36 into 360 tells us that the polygon has 10 exterior angles and, therefore, 10 sides.

If you want to try some challenging problem similar to those you’ll see on ACT test day, you might want to check out our book, 200 Challenging ACT Math Problems, available on Amazon.

If you have questions about this problem or anything else on the ACT, send us an email at .


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