Question

In the given figure,, if ∠DAB = 60∘ , ∠ABD = 50∘ , then ∠ACB = _________

Answer 1

Given:
∠DAB = 60° ...(1)
∠ABD = 50° ...(2)


In ∆ADB,
∠DAB + ∠DBA + ∠ADB = 180° (angle sum property)
⇒ 60° + 50° + ∠ADB = 180° (From (1) and (2))
⇒ ∠ADB = 180° − 110°
⇒ ∠ADB = 70° ...(3)


We know, angles in the same segment of the circle are equal.
Thus, ∠ADB = ∠ACB
⇒ 70° = ∠ACB (From (3))
⇒ ∠ACB = 70°


Hence, ∠ACB = 70°.