Question

Find the measure of the arc or angle indicated PLEASE HELP

Answer 1

Option D.
`<R=62\°`

Explanation:

step 1

Find the measure of angle F

we know that

In an inscribed quadrilateral, the opposite angles are supplementary

so

`<Q+<F=180\°`

substitute the value of <Q

`99\°+<F=180\°`

`<F=180\°-99\°=81\°`

step 2

Find the measure of arc PQ

we know that

The inscribed angle measures half that of the arc comprising

so

`<F=(1)/(2)(arc\ PQ+arc\ RQ)`

substitute values

`81\°=(1)/(2)(arc\ PQ+92\°)`

`162\°=(arc\ PQ+92\°)`

`arc\ PQ=162\°-92\°=70\°`

step 3

Find the measure of angle R

we know that

The inscribed angle measures half that of the arc comprising

so

`<R=(1)/(2)(arc\ FP+arc\ PQ)`

substitute values

`<R=(1)/(2)(54\°+70\°)`

`<R=(1)/(2)(124\°)`

`<R=62\°`