Question

One of the diagonals of a rhombus is equal to a side of the rhombus. The angles of the rhombus are

• A. ${60}^o,{80}^o$
• B. ${60}^o,{120}^o$
• C. ${120}^o,{240}^o$
• D. ${100}^o,{120}^o$

Answer 1

The correct option is B ${60}^o,{120}^o$

$AB=BD=DC=CA=BC=x$

$MC=\frac{x}{2}$

$\left(\frac{c}{2}\right)=\cos \theta =\frac{x/2}{x}=\frac{1}{2}$

$\Rightarrow \theta ={60}^o$

$\frac{c}{2}=60$

$\Rightarrow C=120=B$

$A+B+C+D=360$

$A+D={120}^o$

$A={60}^o$

$\therefore B$ Answer