Question

In Fig. O is the centre of the circle. If ∠APB=50°, find ∠AOB and ∠OAB.

Answer 1

∠APB = 50° (Given) 

By degree measure theorem, 

∠AOB = ∠APB ∠APB = 2 x 50 = 100° 

Since, 

OA = OB (Radii) 

Hence, 

∠OAB = ∠OBA 

(Angle opposite to equal sides are equal) 

Let, 

∠OAB = x 

In Triangle OAB, 

∠OAB + ∠OBA + ∠AOB = 180° 

x + x + 100° = 180° 

2x = 80° 

x = 40° 

∠OAB = ∠OBA = 40°