Question

In figure, O is the centre of the circle. If ∠BOD = 160°, find the values of x and y.

Answer 1

From figure: ∠BOD = 160° 

By degree measure theorem: ∠BOD = 2∠BCD 

160° = 2x

or x = 80°

Now, in quadrilateral ABCD, 

∠BAD + ∠BCD = 180° (Opposite angles of Cyclic quadrilateral) 

y + x = 180°

Putting value of x, y + 80° = 180° 

y = 100° 

Answer: x = 80° and y = 100°.