Question

a square piece of paper is placed at the top of a regular polygon so only the top of the polygon is showing. if x+y=80, how many sides does the polygon have?

Answer 1

Since the two angles that are not a part of the polygon add up to 80, and a quadrilateral's angles add up to 360, you can conclude that the polygon angles add up to 280, and therefore each angle in the polygon is 140.

So, we will have:

$$\frac {(n - 2) \cdot 180}{n} = 140 \Rightarrow 180 \cdot n - 360 = 140 \cdot n \Rightarrow 40 \cdot n = 360 \Rightarrow n = 9.$$

So, this polygon has 9 sides.

Answer: this polygon has 9 sides.