Question

In the following figure , ABCD is a parallelogram . Find the value x,y and z .

Answer 1

From the figure

$AD\parallel BC,BD$ is the transversal line

$⟹\angle ADB=\angle DBC$ $(\because alternateangles)$

$⟹z={30}^{\circ }$

Also

${100}^{\circ },x$ are supplementary angles

So $x={180}^{\circ }-{100}^{\circ }={80}^{\circ }$

$x,y,{30}^{\circ }$ forms a triangle

$⟹x+y+{30}^{\circ }={180}^{\circ }$

$⟹y={180}^{\circ }-{80}^{\circ }-{30}^{\circ }={70}^{\circ }$