This figure shows circle A with inscribed ∠RSQ . m∠RSQ=24° What is the measure of RSQ?

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1 Answer
May 10, 2018

hat (RSQ) = 312°

Explanation:

A conjecture about inscribed angles states the inscribed angle is one half the arc it cuts. The converse is also true; an arc is double the measure of the angle by which is cut.

With this conjecture, we know that hat (RQ) = 2*m/_RQ = 2*24 = 48

A circle must be 360 degrees. Since hat (RSQ) + hat (RQ) = 360, we can also say that hat (RSQ) + 48 = 360, meaning hat (RSQ) = 312