Question

Given: AD≅AO
Find: m∠OAD, m∠DBA.

Answer 1

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

Answer 2

Answer:

Step-by-step 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

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

⇒$m{\angle}DBA=\frac{60^{\circ}}{2}$

⇒$m{\angle}DBA=30^{\circ}$

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