Question

In the given figure, $\angle ABD={54}^{\circ }\text{and}\angle BCD={43}^{\circ },$, calculate

(i) $\angle ACD$

(ii) $\angle BAD$

(iii) $\angle BDA$.

Answer 1

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