Question

Question 172
ABCD is a parallelogram. Find the values of x, y and z.

Answer 1

Given, a parallelogram ABCD
In the $\Delta OBC$, we have
$y+{30}^{\circ }={100}^{\circ }$ [exterior angle property of triangle]
$\Rightarrow y={70}^{\circ }$
By the angle sum property of a triangle,
we have, $x+y+30={180}^{\circ }$
$\Rightarrow x+{70}^{\circ }+{30}^{\circ }={180}^{\circ }\Rightarrow x={180}^{\circ }-{100}^{\circ }={80}^{\circ }$
Now, since $AD\parallel BC$ and BD is transversal, therefore
$\angle ADO=\angle OBC$ [alternate interior angles]
$\Rightarrow z={30}^{\circ }$