Q:

find the measure of the arc or angle indicated PLEASE HELP

Accepted Solution

A:
Answer:Option D. [tex]<R=62\°[/tex]Step-by-step explanation:step 1Find the measure of angle Fwe know thatIn an inscribed quadrilateral, the opposite angles are supplementaryso[tex]<Q+<F=180\°[/tex]substitute the value of <Q[tex]99\°+<F=180\°[/tex][tex]<F=180\°-99\°=81\°[/tex]step 2Find the measure of arc PQwe know thatThe inscribed angle measures half that of the arc comprisingso[tex]<F=\frac{1}{2}(arc\ PQ+arc\ RQ)[/tex]substitute values[tex]81\°=\frac{1}{2}(arc\ PQ+92\°)[/tex][tex]162\°=(arc\ PQ+92\°)[/tex][tex]arc\ PQ=162\°-92\°=70\°[/tex]step 3Find the measure of angle Rwe know thatThe inscribed angle measures half that of the arc comprisingso[tex]<R=\frac{1}{2}(arc\ FP+arc\ PQ)[/tex]substitute values[tex]<R=\frac{1}{2}(54\°+70\°)[/tex][tex]<R=\frac{1}{2}(124\°)[/tex][tex]<R=62\°[/tex]