In the given figure, ∠ACB = 52° and= ∠BDC = 43°. Calculate

(i) ∠ADB

(ii) ∠BAC

(iii) ∠ABC.

(i) From figure,

∠ADB = ∠ACB = 52° [Angles in the same segment are equal]

∠ADB = 52°.

Hence, ∠ADB = 52°.

(ii) From figure,

∠BAC = ∠BDC = 43° [Angles in the same segment are equal]

∠BAC = 43°.

Hence, ∠BAC = 43°.

(iii) We know that,

The sum of the three interior angles of any triangle is always 180°.

⇒ ∠BAC + ∠ABC + ∠ACB = 180°

⇒ 43° + ∠ABC + 52° = 180°

⇒ ∠ABC + 95° = 180°

⇒ ∠ABC = 180° - 95°

⇒ ∠ABC = 85°.

Hence, ∠ABC = 85°.