Question

Find $\angle CAD$ if CA = CD and $\angle ACD={58}^{\circ }$.

• A. 61

Answer 1

The correct option is A 61
Given,
$CA=CD$
$\angle ACD={58}^{\circ }$

Now,
$\angle CAD=\angle ADC$ .. (i)
[ Angles opposite to equal sides are always equal]

In $\Delta ACD$,
$\angle CAD+\angle ADC+\angle ACD={180}^{\circ }$ [Angle Sum Property]
$\angle CAD+\angle CAD+\angle ACD={180}^{\circ }$
[From (i)]
$2\angle CAD+{58}^{\circ }={180}^{\circ }$
$2\angle CAD={122}^{\circ }$
$\angle CAD={61}^{\circ }$