Question

In the diagram, m of angle Q= 75º and Measure of arc QS = 133 degrees. Find Measure of QR. PLEASE HELP!

Answer 1

It is given that angle Q is 75 degrees and arc QS is 133 degrees.

Use inscribed angle theorem on angle RQS to get:

`\begin{gathered} \angle RQS=(1)/(2)mRS \\ m(RS)=2\angle RQS \\ m(RS)=2*75=150^(\circ) \end{gathered}`

It is known that the sum of all arcs of circle is 360 degrees so it follows:

`\begin{gathered} m(QS)+m(RS)+m(RQ)=360 \\ 133+150+m(RQ)=360 \\ m(RQ)=360-150-133=77^(\circ) \end{gathered}`

Hence the measure of arc QR is 77 degrees.

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