Question

Use the diagram to find the measure of each of the angles.

Answer 1

LOQ is 80

LRQ is 40

LBQ is 40


good luck

Answer 2

Part 1)
`m<LOQ=80\°`

Part 2)
`m<LRQ=40\°`

Part 3)
`m<LBQ=40\°`

Explanation:

Part 1) Find the measure of angle LOQ

we know that

`m<LOQ=m\ arc\ QL` -----> by central angle

we have that

`m\ arc\ QL=80\°`

so

`m<LOQ=80\°`

Part 2) Find the measure of angle LRQ

we know that

The inscribed angle measures half that of the arc comprising

so

`m<LRQ=(1/2)m\ arc\ QL`

we have

`m\ arc\ QL=80\°`

substitute

`m<LRQ=(1/2)80\°=40\°`

Part 3) Find the measure of angle LBQ

we know that

The inscribed angle measures half that of the arc comprising

so

`m<LBQ=(1/2)m\ arc\ QL`

we have

`m\ arc\ QL=80\°`

substitute

`m<LBQ=(1/2)80\°=40\°`