Question

The sum of the interior angles of Michael’s polygon equals 180°. The sum of the interior angles of Cary’s polygon equals 360°. How many MORE sides does Cary’s polygon have than Michael’s polygon?
A. 1 side
B. 2 sides
C. 3 sides
D. 4 sides

Answer 1

Recall that for a polygon to have 180° as the sum of its interior angles, then it must have three sides and thus a triangle. And similarly, for a polygon to have a sum of 360°, it must have four sides or it is a quadrilateral.

[Note that for larger angles, we can apply the formula 180(n - 2) to find the total sum of the interior angles. n is the number of sides]

Now, since we're comparing a four-sided and three-sided polygon, this means that they only differ by 1 side. 

Answer: A. 1 side