Question

find the measure of the missing angles.

Explanation:

Step1: Note right - angle relationship

Since the angle formed by two perpendicular lines is 90°, for the angle composed of the 28° angle and \(x\), we have \(x + 28^{\circ}=90^{\circ}\).

Step2: Solve for \(x\)

Subtract 28° from both sides of the equation: \(x=90^{\circ}- 28^{\circ}=62^{\circ}\).

Step3: Note linear - pair relationship

The angle \(y\) and \(x\) form a linear - pair (a straight - line angle which is 180°). So \(y + x=180^{\circ}\).

Step4: Solve for \(y\)

Substitute \(x = 62^{\circ}\) into the equation: \(y=180^{\circ}-x\), then \(y = 180^{\circ}-62^{\circ}=118^{\circ}\).

Answer:

\(x = 62^{\circ}\), \(y = 118^{\circ}\)