Question

In the given figure, $AD=AE$ and $\angle BAD=\angle EAC$, then

• A. $x=11$
• B. $x=13$
• C. $y=21$
• D. $y=11$

Answer 1

The correct option is A $x=11$

$\Delta ADE$ is isosceles (as $AD=AE$ given)

so, $\angle ADE=\angle AED$

${180}^o-\angle ADE={180}^o-\angle AED$

$\angle ADB=\angle AEC$

Now in $\Delta ADB$ and $\Delta AEC$

$angleBAD=\angle EAC$ (given)

$AD=AE\left(given\right)$

$\angle ADB=\angle AEC\left(proved\right)$

$\therefore \angle ADB=\angle AEC$ (ASA congruence)

so $AB=AC$ and $BD=CE$ (cpct)

or $2y+3=43$ and $x-1=10$

so $y=20,x=11$