Question

Given: line AD≅ line AO

Find: m∠OAD, m∠DBA.


Please Help!

Answer 1

Part 1)
`m<OAD=60\°`

Part 2)
`m<DBA=30\°`

Explanation:

Part 1) Find the measure of angle OAD

we know that

OA=OD=radius of the circle

If line AD≅ line AO

then

The triangle AOD is an equilateral triangle

Remember that

An equilateral triangle has the three equal sides and the three internal angles equal (60 degrees each one)

so

`m<OAD=60\°`

Part 2) Find the measure of angle DBA

we know that

The inscribed angle measures half that of the arc comprising

so

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

`arc\ AD=m<AOD=60\°` ----> by central angle

substitute the value

`m<DBA=(1)/(2)(60\°)=30\°`