Question

find the measure of the missing angles.

Explanation:

Step1: Use right - angle property

Since the vertical line and the horizontal line form a right - angle (90°), and one part of the right - angle is 28°. We can find angle $x$ by subtracting 28° from 90°.
$x = 90^{\circ}-28^{\circ}$

Step2: Calculate $x$

$x = 62^{\circ}$

Step3: Use straight - line property

The straight - line has an angle of 180°. Angle $y$ and angle $x$ form a straight - line. So we can find angle $y$ by subtracting angle $x$ from 180°.
$y=180^{\circ}-x$

Step4: Substitute $x$ value to find $y$

Substitute $x = 62^{\circ}$ into the equation for $y$.
$y = 180^{\circ}-62^{\circ}=118^{\circ}$

Answer:

$x = 62^{\circ}$, $y = 118^{\circ}$