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 $m\angle PQR$?
Not totally sure about this....but.....look at the following image :
We can anchor Q and R at two consecutive points on the circle....... PQR will have five possible values........
Let P be positioned at P1 and PQR will can be an inscribed angle measuring (5/7) of 180°
Let P be positioned at P2 and PQR will be an inscribed angle measuring (4/7) of 180°
Lastly.....let P be positioned at P5 and PQR will be an inscribed angle measuring (1/7) of 180°