Question

1. find the degree measures $x$ and $y$ of the missing angles in the diagram below.

Explanation:

Step1: Find angle $x$

Vertical angles are equal, so $x = 90^\circ + 20^\circ = 110^\circ$.

Step2: Find angle $y$

Angles on a straight line sum to $180^\circ$.
$y = 180^\circ - (90^\circ - 20^\circ) = 180^\circ - 70^\circ = 110^\circ$.
Alternatively, $y$ and $x$ are vertical angles, so $y=x=110^\circ$.

Answer:

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