Question

Given: AD≅AO
Find: m∠OAD, m∠DBA.

Answer 1

`OA=OD=AD=R\Rightarrow \bigtriangleup OAD\: is\: an\: equilateral\: triangle \\ \Rightarrow \widehat{AOD}=\widehat{OAD}=\widehat{ODA}=60° \\ \widehat{ABD}= \frac{\widehat{AOD}}{2} = (60°)/(2) = 30°`

Answer 2

Explanation:

Given: AD≅AO

To find: m∠OAD and m∠DBA.

Solution: It is given that AD≅AO, and also OA≅OD (Radius of circle), therefore ΔAOD is an equilateral triangle.

Hence, m∠OAD=m∠ODA=m∠AOD=60°.

Now, we know that the intercepted angle is half of the central angle, thus

`m{\angle}DBA=\frac{m{\angle}AOD}{2}`

⇒
`m{\angle}DBA=(60^(\circ))/(2)`

⇒
`m{\angle}DBA=30^(\circ)`

Hence, the measures of
`{\angle}OAD` and
`{\angle}DBA` are
`60^(\circ)` and
`30^(\circ)` respectively.