In the given figure, ∠ABD = 54° and ∠BCD = 43°, calculate (i) ∠ACD (ii) ∠BAD (iii) ∠BDA.

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Solution

(i)
We know that the angles in the same segment of a circle are equal.
i.e., ∠ABD = ∠ACD = 54°

(ii)
We know that the angles in the same segment of a circle are equal.
i.e., ∠BAD = ∠BCD = 43°

(iii)
In ΔABD, we have:
∠BAD + ∠ADB + ∠DBA = 180° (Angle sum property of a triangle)
⇒ 43° + ∠ADB + 54° = 180°
⇒ ∠ADB = (180° – 97°) = 83°
⇒ ∠BDA = 83°

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