Question

In the given figure, $AB\parallel CD$ and $CA=CE$. Find the value of $x$, $y$ and $z$.

• A. $x=36$, $y=68$, $z=44$
• B. $x=36$, $y=44$, $z=68$
• C. $x=44$, $y=68$, $z=36$
• D. $x=68$, $y=36$, $z=44$

Answer 1

The correct option is A $x=36$, $y=68$, $z=44$

Given: $AB\parallel CD$
$\angle BAD=\angle CDA={36}^{\circ }$ (Alternate angles)
$\angle AEC=\angle ECD+\angle EDC$ (Exterior angle property)
$\angle AEC=32+36$
$\angle AEC={68}^{\circ }$
Since, $AC=AE$
$y=\angle AEC={68}^{\circ }$ (Isosceles triangle property)
In $△ACE$
$\angle ACE+\angle AEC+\angle CAE=180$ (Angle sum property)
$z+68+68=180$
$z=180-136$
$z={44}^{\circ }$