nA = 360
The measure A, in degrees, of an exterior angle of a regular polygon is related to the number of sides, n, of the polygon by the formula above. If the measure of an exterior angle of a regular polygon is greater than 50°, what is the greatest number of sides it can have?

Options

A. 5
B. 6
C. 7
D. 8

Explanation

Choice C is correct. The relationship between n and A is given by the equation nA = 360. Since n is the number of sides of a polygon, n must be a positive integer, and so nA = 360 can be rewritten as `A=(360)/(n)`. If the value of A is greater than 50, it follows that `(360)/(n) gt 50` is a true statement. Thus, 50n lt 360, or `n lt (360)/(50)`. Since n must be an integer, the greatest possible value of n is 7.
Choices A and B are incorrect. These are possible values for n, the number of sides of a regular polygon, if A gt 50, but neither is the greatest possible value of n. Choice D is incorrect. If A lt 50, then n = 8 is the least possible value of n, the number of sides of a regular polygon. However, the question asks for the greatest possible value of n if A gt 50, which is n = 7.