Suppose we are given seven points that are equally spaced around a circle. If P, Q, and R are chosen to be any three of these points, then how many different possible values are there for angle PQR?

Mathgenius
Sep 22, 2018

#1**+1 **

There are a total of \(\dbinom{6}{2}=15\) possible angles

But it turns out that many of the angles are congruent.

The 15 angles are made up of 1 + 2 + 3 + 4 + 5 copies of 5 different angles.

There are only 5 different possible angles

Rom
Sep 23, 2018

#2**+1 **

I've played with this a little and Rom's answer is most likely correct but I do not see why.

If I spent hours on proofs I am sure I could show it but I don't see it intuitively at all.

I was surprised when that angle came up as 77 degrees.

Melody
Sep 23, 2018