Question

Side AB of a quadrilateral is a diameter of its circumcircle and ∠ADC = 140°, then ∠BAC equals

(a) 80°

(b) 50°

(c) 40°

(d) 30°

Answer 1

Answer is (b) 50°

ABCD is a cyclic quadrilateral

∴ ∠D + ∠B = 1800

∠B = 180° – ∠D

∠B = 180° – 140°

∠B = 40°

∠ACB is angle in semicircle

∴ ∠ACB = 90°

Now in ∆ABC

∠ABC + ∠ACB + ∠BAC = 180°

⇒ 40° + 90° + ∠BAC = 180°

⇒ ∠BAC= 180° – (40° + 90°)

⇒ ∠BAC= 180° – 130°

⇒ ∠BAC = 50°