Question

Using the information given in the figure, the 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 $△BAD$ and $△ADC$,
$\angle BAD$ = $\angle CAD$ .........(given)
AD = AD .......(common)
$\angle ADB=\angle ADC={90}^{\circ }$ .......(given)
$\therefore$ $△ABD\cong △ACD$ .......(ASA Postulate)
AB = AC .......(CPCT)
$\Rightarrow 3x-22=38$
$\Rightarrow 3x=60$
$\Rightarrow$ $x=20$
Also, $\angle ABD=\angle ACD$ ........(CPCT)
$\Rightarrow 3y-{25}^{\circ }={75}^{\circ }-y$
$\Rightarrow 4y={100}^{\circ }$
$\Rightarrow$ $y={25}^{\circ }$
$\therefore$ $x=20$ , $y={25}^{\circ }$