Question

ABCD is a rhombus if $\angle A={65}^{\circ }$, find $\angle CDB$.

• A. ${37}^{\circ }$
• B. ${57.5}^{\circ }$
• C. ${55.5}^{\circ }$
• D. ${75}^{\circ }$

Answer 1

The correct option is B ${57.5}^{\circ }$


Given that, $\angle DAB={65}^{\circ }$
So, $\angle DCB={65}^{\circ }$ [opposite angles of a parallelogram is equal]
Let $\angle CDB=x^{\circ }$
In $△CDB$, we have $CD=CB$ [In rhombus all sides are equal]
So,
$\angle CBD=\angle CDB=x^{\circ }$ [opposite angles of equal sides are equal]
In $△CDB$,
$\angle CBD+\angle CDB+\angle DCB={180}^{\circ }$ [By angle sum property]
$\Rightarrow x^{\circ }+x^{\circ }+{65}^{\circ }={180}^{\circ }$
$\Rightarrow 2x^{\circ }={115}^{\circ }$
$\Rightarrow x^{\circ }={57.5}^{\circ }$
Therefore,
$\angle CDB={57.5}^{\circ }$