Using the 2 tangents line formula:
[tex]m\angle Q=\frac{1}{2}((360-mPR)-mPR)[/tex]
[tex]\begin{gathered} 81x-1=\frac{1}{2}(360-2(100x)) \\ 81x-1=\frac{1}{2}(360-200x) \\ 81x-1=180-100x \\ \end{gathered}[/tex]
Solve for x:
[tex]\begin{gathered} 81x+100x=1+180 \\ 181x=181 \\ x=\frac{181}{181} \\ x=1 \end{gathered}[/tex]
Therefore:
[tex]\begin{gathered} mPR=100(1)_{} \\ mPR=100 \end{gathered}[/tex]
Answer:
A. 100
