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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 $m\angle PQR$?

 Sep 26, 2017

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°



cool cool cool

 Sep 26, 2017

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