Question

in the fig o is the centre of the circle &A,B,C,D are points on the circle angle ADC=120° find x​

Answer 1

We know that, sum of the opposite angles in a cyclic quadrilateral is 180°

∠ADC + ∠ABC = 180°

∠ADC + ∠ABC = 180°

⇒ 126° + ∠ABC = 180°

⇒ 126° + ∠ABC = 180°

⇒ ∠ABC = 180 − 126°

∠ABC = 54°

Since, ∠ACB

∠ACB is an angle in a semi–circle.

∠ACB = 90°

In ΔABC, ∠BAC + ∠ACB + ∠ABC = 180°

ΔABC, ∠BAC + ∠ACB + ∠ABC = 180° [by angle sum property of a triangle]

⇒ ∠BAC = 90° + 54° = 180°

⇒ ∠BAC = 90° + 54° = 180°

⇒ ∠BAC = 180° − 144° = 36°