offers hundreds of practice questions and video explanations. Go there now.
Sign up or log in to Magoosh GRE Prep.

Magoosh Brain Twister: Sidesplitting Fun – Explanation


Refresh your memory, then let’s get started on this week’s Brain Twister explanation!


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

Numeric Entry: _______________________


Answer and Explanation

To maximize the value of ‘t’, we first need to shift our attention to ‘s’, the angle measure of Polygon X. We know that ‘s’ is an integer, so imagine the exterior angle of this massive polygon. The smallest number that could be is 1 degree, leaving us 179 degrees for the interior angle of the polygon.

Alternatively, we could use the formula 180(r – 2)/r, since we are dealing with a congruent polygon (each side is the same, so we can divide by ‘r’ to find the degree measure of any one angle). You can try out the largest possible integer, 179, to see that it works. We learn that ‘r’ is equal to 360 sides so Polygon X has 360 sides.

Polygon Q, therefore, has 90 sides. Since, the ‘r’ above, stands for number of sides (it doesn’t really matter what we call the variable), we get 180(90-2)/90 = 2 x 88 = 176.

Congrats to those who got the correct answer. 🙂


See you again soon!


By the way, students who use Magoosh GRE improve their scores by an average of 8 points on the new scale (150 points on the old scale.) Click here to learn more.

No comments yet.

Magoosh blog comment policy: To create the best experience for our readers, we will only approve comments that are relevant to the article, general enough to be helpful to other students, concise, and well-written! 😄 Due to the high volume of comments across all of our blogs, we cannot promise that all comments will receive responses from our instructors.

We highly encourage students to help each other out and respond to other students' comments if you can!

If you are a Premium Magoosh student and would like more personalized service from our instructors, you can use the Help tab on the Magoosh dashboard. Thanks!

Leave a Reply