Question

Mark (✓) against the correct answer in each of the following:
In the given figure, the measure of ∠BCD is
(a) 100°
(b) 70°
(c) 80°
(d) 30°

Answer 1

(c) 80°

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