Question

Find the value of $x,y$ and $z$ from the given parallelograms.

Answer 1

$\angle PQR+ext.\angle Q={180}^{\circ }$ [Linear pair]

$\angle PQR+{80}^{\circ }={180}^{\circ }\Rightarrow \angle PQR={100}^{\circ }$

$x+{100}^{\circ }={180}^{\circ }$ [Supplementary angles of parallelogram]

$x={80}^{\circ }$

In $△PSR,Z=\angle SRP$ [Alternate angles]

$\therefore {80}^{\circ }+{60}^{\circ }+Z={180}^{\circ }\Rightarrow Z={180}^{\circ }-{140}^{\circ }={40}^{\circ }$

In $△PQR$,

${40}^{\circ }+y+{100}^{\circ }={80}^{\circ }$

$y={180}^{\circ }-{140}^{\circ }={40}^{\circ }$