In Fig. 10.7, if

Given: ∠DAB = 60°, ∠ABD = 50°

Using the theorem “angles in the same segment of the circle are equal”:

∴ ∠ADB = ∠ACB ……………… (1)

In triangle ABD, using the angle sum property of triangle, we have:

∠ABD + ∠ADB +∠DAB = 180°

⇒ 50° + ∠ADB + 60° = 180°

⇒ ∠ADB = 180° - 50° - 60°

⇒ ∠ADB = 70°

∴ From equation (1), we have:

∠ACB = 70°