Question

In a rhombus ABCD, if $\angle ACB={40}^{\circ }$, then $\angle ADB=$

• A. ${70}^{\circ }$
• B. ${45}^{\circ }$
• C. ${50}^{\circ }$
• D. ${60}^{\circ }$

Answer 1

The correct option is

C

${50}^{\circ }$

In rhombus ABCD, $\angle ACB={40}^{\circ }$

$\therefore \angle BCD=2\times \angle ACB=2\times {40}^{\circ }={80}^{\circ }But\angle BCD+\angle ADC={180}^{\circ }\left(\text{Sum of consecutive angles of}||gm\right)\Rightarrow {80}^{\circ }+\angle ADC={180}^{\circ }\Rightarrow \angle ADC={180}^{\circ }-{80}^{\circ }={100}^{\circ }\therefore \angle ADB=\frac{1}{2}\angle ADC=\frac{1}{2}\times {100}^{\circ }={50}^{\circ }$