Question

In the figure given below, find the measure of the angles denoted by $x,y,z,p,q$ and $r$.

Answer 1

$x={180}^{\circ }-{100}^{\circ }\text{(Linear pair of angles)}$
$x={80}^{\circ }$
$y=x$ (Alternate exterior angles)
$y={80}^{\circ }$
$z={100}^{\circ }$ (Corresponding angles)
$p=x$ (Vertically opposite angles)
$p={80}^{\circ }$
$q={100}^{\circ }$ (Vertically opposite angles)
$r=q$ (Corresponding angles)
$r={100}^{\circ }$
Therefore, the measure of angles are,
$x=y=p={80}^{\circ }$
$q=r=z={100}^{\circ }$