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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,

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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\$?

Guest Sep 26, 2017
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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°

CPhill  Sep 26, 2017

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