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

hat (RSQ) = 312°
With this conjecture, we know that $\hat{R Q} = 2 \cdot m \angle R Q = 2 \cdot 24 = 48$
A circle must be 360 degrees. Since $\hat{R S Q} + \hat{R Q} = 360$, we can also say that $\hat{R S Q} + 48 = 360$, meaning $\hat{R S Q} = 312$