Question

for questions 8 - 10, in the diagram below, \overleftrightarrow{ab} is parallel to \overleftrightarrow{cd}. use the diagram to find the unknown angles.

1. find x
2. find y
3. find z

Explanation:

Step1: Find $x$ (corresponding angles)

Since $\overleftrightarrow{AB} \parallel \overleftrightarrow{CD}$, corresponding angles are equal.
$x = 70^\circ$

Step2: Find $y$ (supplementary to $x$)

$x$ and $y$ form a linear pair, so they add to $180^\circ$.
$y = 180^\circ - x = 180^\circ - 70^\circ = 110^\circ$

Step3: Find $z$ (vertical/alternate angles)

$z$ is vertical to $x$, or alternate to the $70^\circ$ angle, so they are equal.
$z = x = 70^\circ$

Answer:

$x = 70^\circ$, $y = 110^\circ$, $z = 70^\circ$