In Fig. 16.120, O is the centre of the circle. If ∠APB=50°, find ∠AOB and ∠OAB.
∠APB = 50o (Given)
By degree measure theorem,
∠AOB = ∠APB
∠APB = 2 * 50
= 100o
Since,
OA = OB (Radii)
Hence,
∠OAB = ∠OBA (Angle opposite to equal sides are equal)
Let,
∠OAB = x
In Triangle OAB,
∠OAB + ∠OBA + ∠AOB = 180o
x + x + 100o = 180o
2x = 80o
x = 40o
∠OAB = ∠OBA = 40o