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Question
In the below fig. O is the centre of the circle. If ∠APB = 50°, find ∠AOB and ∠OAB.
Solution
ΔAPB = 50°
By degree measure theorem
∠AOB=2 ∠APB
⇒∠APB= 2 × 50° = 100°
Since OA =OB
[ Radius of circle ]
Then ∠OAB=∠OBA
[ Angle's opposite to equal sides ]
Let ∠OAB = x
In Δ OAB by angle sum property
`∠OAB+∠OBA+∠AOB=180°`
`⇒x+x+100=180°`
`⇒2x+100=180°`
`⇒2x=80°`
`⇒x=40°`
`∠OAB =∠OBA= 40°`
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