Question

find the measure of the missing angles. answer x = y =

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 45°. We know that for angle \(x\), \(x + 45^{\circ}=90^{\circ}\).
So, \(x=90^{\circ}- 45^{\circ}\).

Step2: Use linear - pair property

The sum of angles on a straight line is 180°. The angle adjacent to \(y\) and the 45° angle and \(x\) together form a straight line. Since \(x = 45^{\circ}\), and the sum of the angles in that part of the straight - line is \(x + 45^{\circ}+y=180^{\circ}\). Substituting \(x = 45^{\circ}\), we get \(45^{\circ}+45^{\circ}+y=180^{\circ}\), then \(y=180^{\circ}-(45^{\circ}+45^{\circ})\).

Answer:

\(x = 45\)
\(y = 135\)