Question

Given that AB is a diameter of circle O, find the missing angle arc measures.

Answer 1

Part 1)
`m\ arc\ CB=64\°`

Part 2)
`m<AOC=116\°`

Part 3)
`m\ arc\ AD=26\°`

Part 4)
`m\ arc\ DFB=154\°`

Part 5)
`m<CDB=32\°`

Explanation:

Part 1) Find the measure of arc CB

we know that

`m\ arc\ CB=m<COB` -----> by central angle

we have

`m<COB=64\°` ----> given problem

so

`m\ arc\ CB=64\°`

Part 2) Find the measure of angle AOC

we know that

`m<AOC+m<COB=180\°` ------> by supplementary angles

we have

`m<COB=64\°`

substitute

`m<AOC+64\°=180\°`

`m<AOC=180\°-64\°=116\°`

Part 3) Find the measure of arc AD

we know that

The inscribed angle measures half that of the arc comprising

so

`m<ABD=(1)/(2)(m\ arc\ AD)`

we have

`m<ABD=13\°`

substitute

`13\°=(1)/(2)(m\ arc\ AD)`

`m\ arc\ AD=26\°`

Part 4) Find the measure of arc DFB

we know that

`m\ arc\ DFB=360\°-(m\ arc\ AD+m\ arc\ ACB)`

we have

`m\ arc\ AD=26\°`

`m\ arc\ ACB=180\°` -----> because is a diameter

substitute

`m\ arc\ DFB=360\°-(26\°+180\°)=154\°`

Part 5) Find the measure of angle CDB

we know that

The inscribed angle measures half that of the arc comprising

so

`m<CDB=(1)/(2)(m\ arc\ CB)`

we have

`m\ arc\ CB=64\°`

substitute

`m<CDB=(1)/(2)(64\°)=32\°`