Question

If O is the centre of the circle, find the value of x in the figure.

Answer 1

∠DBO = 40° (Given) 

Form figure: 

∠DBC = 90° [Angle in a semicircle] 

∠DBO + ∠OBC = 90° 

40° +∠OBC = 90° 

or ∠OBC = 90° − 40° = 50° 

Again, By degree measure theorem: 

∠AOC = 2∠OBC 

or x = 2 x 50° = 100°