Question

Mark (✓) against the correct answer in each of the following:
In the given figure, ABCD is rhombus in which ∠A = 70°. Then, ∠CDB = ?
(a) 35°
(b) 20°
(c) 55°
(d) 50°

Answer 1

(c) 55°

$$\begin{gathered} \mathrm{ABCD}\mathrm{is}\mathrm{a}\mathrm{rhombus}. \\ \mathrm{So},CD\parallel AB. \\ \angle DAB+\angle ADC=180°(\text{A}\mathrm{ngles}\mathrm{on}\mathrm{the}\mathrm{same}\mathrm{side}\mathrm{of}\mathrm{a}\mathrm{transversal}) \\ \Rightarrow \angle ADC=180°-\angle DAB=180°-70°=110° \\ \text{We}\mathrm{know}\mathrm{that}\mathrm{the}\mathrm{diagonals}\mathrm{of}\text{a}\mathrm{rhombus}\mathrm{bisect}\mathrm{its}\mathrm{angle}s. \\ \mathrm{So},\angle CDB=\frac{1}{2}\angle ADC \\ =\frac{1}{2}\times 110° \\ =55° \end{gathered}$$