Q1 of 100 Page 17

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


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