Question

The circle below has center S. Suppose that mQR= 106°. Find the following(a) m

Answer 1

We have to find the measure of the angle QSR and the angle QPR.

The angle QSR is a central angle. This means that

`\begin{gathered} m\hat{QR}=m\measuredangle QSR \\ m\measuredangle QSR=106^(\circ) \end{gathered}`

The angle QPR is an inscribed angle, thus:

`\begin{gathered} m\measuredangle QPR=(1)/(2)m\hat{QR} \\ m\measuredangle QPR=(1)/(2)\cdot106^(\circ)=53^(\circ) \end{gathered}`

This means that m∡QSR=106° and m∡QPR=53°.