Question

Mark (✓) against the correct answer in each of the following:
In the given figure, ∠ABC = 70° and ∠ACB = 30°. Then, ∠BDC = ?
(a) 70°
(b) 60°
(c) 80°
(d) 90°

Answer 1

(c) 80°

$$\begin{gathered} \mathrm{We}\mathrm{know}\mathrm{that}\mathrm{angles}\mathrm{in}\mathrm{the}\mathrm{same}\mathrm{segment}\mathrm{are}\mathrm{equal}. \\ \mathrm{So},\angle BAC=\angle BDC \\ \mathrm{In}∆ABC, \\ \angle ABC+\angle ACB+\angle BAC=180°(\text{A}\mathrm{ngle}\mathrm{sum}\mathrm{property}) \\ \Rightarrow \angle BAC=180°-\angle ABC-\angle ACB \\ \Rightarrow \angle BAC=180°-70°-30° \\ \Rightarrow \angle BAC=80° \\ \mathrm{Hence},\angle BAC=\angle BDC=80°. \end{gathered}$$