Question

In the given figure, AE || BD, AC || ED and AB = AC. Find $\angle a$ in degrees.

Answer 1

$\angle EDC={58}^{\circ }$ (Vertically opposite angles)
Given $AE\parallel CD$
$c=\angle EDC={58}^{\circ }$ (Corresponding angles)
Also, $AC\parallel ED$
$\angle ACB={58}^{\circ }$ (Corresponding angles)
Since, $AB=AC$
$\angle ABC=\angle ACB$ (Isosceles triangle property)
$b=\angle ABC={58}^{\circ }$ (Corresponding angles)
Now, In $△ABC$,
$\angle ABC+\angle ACB+\angle BAC=180$
$58+58+\angle BAC=180$
$\angle BAC=180-116$
$\angle BAC={64}^{\circ }$
$a={64}^{\circ }$