In the given figure, and calculate

(i) (ii) (iii)

(i)

∠ABD and ∠ACD are in the segment AD.

∴ ∠ACD = ∠ABD [Angles in the same segment of a circle]

∠ACD = 54°

(ii) ∠BAD = 43°

∠BAD and ∠BCD are in the segment BD.

∴ ∠BAD = ∠BCD [Angles in the same segment of a circle]

∠BAD = 43°

(iii)

In triangle ABD,

∠ABD + ∠BAD + ∠BAD = 180°[Sum of angles of triangle]

⇒ 54° + 43° + ∠BAD = 180°

⇒ 97° + ∠BAD = 180°

⇒ ∠BAD = 83°