Question

In the given figure, $\angle ADB=\angle ADC={90}^{\circ }.$ Also if $\angle BAD=\angle DAC$ then values of x and y are:

• A. $x=15,y={100}^{\circ }$
• B. $x=60,y={25}^{\circ }$
• C. $x=20,y={25}^{\circ }$
• D. $x=20,y={100}^{\circ }$

Answer 1

The correct option is C $x=20,y={25}^{\circ }$

$In\Delta BADand\Delta ADC,$
$\angle BAD=\angle CAD.......\left(given\right)$
AD = AD.......(common)
$\angle ADB=\angle ADC={90}^{\circ }.......\left(given\right)$
$\therefore \Delta ABD\cong \Delta ACD.......\left(ASAPostulate\right)$
$AB=AC.......\left(CPCT\right)$
$\Rightarrow 3x-22=38$
$\Rightarrow 3x=60$
$\Rightarrow x=20$
Also, $\angle ABD=\angle ACD.......\left(CPCT\right)$
$\Rightarrow 3y-{25}^{\circ }={75}^{\circ }-y$
$\Rightarrow 4y={100}^{\circ }$
$\Rightarrow y={25}^{\circ }$
$\therefore x=20,y={25}^{\circ }$