Question

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

Answer 1

`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`