Question

In the given below the figure, O is the centre of the circle and ∠ AOC = 160°. Prove that 3∠y - 2∠x = 140°.

Answer 1

We know that angle by the same arc at circle i.e., on the circumference is half of the angle by the same arc at the center.
∵ ∠x = `1/2` x 160° = 80°        ....(Opposite triangles of a cyclic quadrilateral supplementary)
∴ ∠x + ∠y = 180° 
∴ ∠y = 100° 

∴ 3∠y - 2∠x
= 3 x 100° - 2 x 80°
= 300° - 160°
= 140°.