given: the measure of arc QR is
[tex]100^o[/tex]find: the measure of angle PQR.
Explanation:
[tex]\begin{gathered} m\angle RPQ=(\frac{1}{2}_)(mQR) \\ =(\frac{100^{\circ}}{2}) \\ =50^o \end{gathered}[/tex]triangle PQR is a right triangle ,
[tex]\begin{gathered} \angle PQR=90^o \\ \end{gathered}[/tex]we know that the sun of interior angles of the triangle is always equals to
[tex]180^o[/tex]so,
[tex]\begin{gathered} \angle PRQ+\angle PQR+\angle RPQ=180^o \\ 90^o+\angle PQR+50^o=180^o \\ \angle PQR=180^o-140^o \\ \angle PQR=40^o \end{gathered}[/tex]Final answer: the measure of angle PQR is 40 degree.