Regular polygon X has r sides, and each vertex has an angle measure of s, an integer. If regular polygon Q...

BTGmoderatorLU wrote: ↑

Sat Nov 14, 2020 11:57 am

Source: Magoosh

Regular polygon X has r sides, and each vertex has an angle measure of s, an integer. If regular polygon Q has r/4 sides, what is the greatest possible value of t, the angle measure of each vertex of Polygon Q?

A. 2
B. 160
C. 176
D. 178
E. 179

The OA is C

Solution:

Recall that the greater the number of sides a regular polygon has, the larger the angle measure of each vertex angle, in degrees. For example, the angle measure of each angle of an equilateral triangle is 60 degrees, that of a square is 90 degrees, that of a regular pentagon is 108 degrees, etc. Therefore, if we want the greatest possible value of t, we want the greatest possible value of s. The greatest number of sides a regular polygon could have, while the degree measure of each of its angles is an integer, is 360. In that case, each of its interior angles is 179 degrees (since each exterior angle is 360/360 = 1 degree). We see that regular polygon X has r = 360 sides, and therefore, regular polygon Q has 360/4 = 90 sides. For a 90-sided regular polygon, each of its exterior angles is 360/90 = 4 degrees. Therefore, each of its interior angles is 180 - 4 = 176 degrees. That is, t = 176.

Answer: C