Question

In the given figure, what is the measure of angle ADC?

• A. $20°$
• B. $85°$
• C. $95°$
• D. $118°$

Answer 1

The correct option is C $95°$

In $\Delta ABC$ and $\Delta ADC$
$AB=AD$ (given)
$BC=DC$ (given)
$AC=AC$ (common)
$\therefore \Delta ABC\cong \Delta ADC$ (by SSS congruence criterion)

$\Rightarrow \angle DAC=\angle BAC=x$ (CPCT)
$\Rightarrow \angle DCA=\angle BCA=y$ (CPCT)
$\angle A={118}^0\Rightarrow x+x={118}^0\Rightarrow x={59}^0$
$\angle C={52}^0\Rightarrow y+y={52}^0\Rightarrow y={26}^0$
In $\Delta ADC,x+y+z={180}^0$ (by angle sum property)
$\Rightarrow {59}^0+{26}^0+z={180}^0$
$\Rightarrow z={180}^0-{85}^0$
$\Rightarrow z={95}^0$
$\therefore \angle ADC=z={95}^0$
So, the correct answer is option (c).