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# Magoosh Brain Twister: Sidesplitting Fun – Explanation

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

## Question

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!

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