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