Question

Find the measure of angles x,y,z and a in the following parallelograms .

Answer 1

We know that adjacent angles of a parallelogram $ABCD$ are supplementary.

$\therefore \angle A+z={180}^{\circ }$

$\Rightarrow z={180}^{\circ }-{120}^{\circ }={60}^{\circ }$

We We know that opposite angles of a parallelogram $ABCD$ are equal.

$\therefore z=\angle CDA={60}^{\circ }$ and $\angle BAD=\angle BCD={120}^{\circ }$

$\angle B=z+a={180}^{\circ }$(linear pair)

$\Rightarrow a={180}^{\circ }-z={180}^{\circ }-{60}^{\circ }={120}^{\circ }$

$\Rightarrow x+\angle DCB={180}^{\circ }$(linear pair)

$\Rightarrow x={180}^{\circ }-\angle DCB={180}^{\circ }-{120}^{\circ }={60}^{\circ }$

$\Rightarrow y+\angle CDA={180}^{\circ }$(linear pair)

$\Rightarrow y={180}^{\circ }-\angle CDA={180}^{\circ }-{60}^{\circ }={120}^{\circ }$

$\therefore a={120}^{\circ },z={60}^{\circ },x={60}^{\circ },y={120}^{\circ }$