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Here is an interesting question

If a regular convex polygon has 'n' sides, then how many different values can 'n' take for which the interior angle of the polygon will be an integer?
A. 16
B. 18
C. 36
D. 24
E. 22

n=22

The answer is absolutely correct.

The sum of an interior angle and corresponding exterior angle is 180 in any polygon. Therefore, if the interior angle is an integer so will the exterior angle be. The sum of all exterior angles of a convex polygon is 360.

The number of sides of a polygon is an integer. In this case, the exterior angle is also an integer. The product of the number of sides and each exterior angle will therefore be 360.

Therefore, it essentially boils down to finding out all positive integer factors for 360.

360 has a total of 24 factors. A polygon has to have a minimum of 3 sides and it therefore eliminates the possibility of 'n' taking values of 1 or 2.

Hence, the different values that are possible are 24 - 2 = 22