Question

If $ABCD$ is a rhombus and if $\angle A={76}^{\circ }$, find $\angle CDB$

Answer 1

Let the measure of $\angle CDB$ be $x.$

As we know that, opposite angles of a rhombus are equal. So,

$\angle A=\angle C={76}^{\circ }$

In $△CDB,$

All sides of a rhombus are equal so, $CD=CB.$ Hence, by using the property that the angles opposite to equal sides of a triangle are also equal.

$\angle CBD=\angle CBD=x$

Now, by using angle sum property,
$\angle CBD+\angle CBD+\angle DCB={180}^{\circ }$
$\Rightarrow 2x^{}+{76}^{}={180}^{\circ }$

$\Rightarrow 2x={104}^{\circ }$
$\Rightarrow x^{}={52}^{\circ }$

$\therefore \angle CBD={52}^{\circ }$