Question

question find the measure of the missing angles. answer

Explanation:

Step1: Use angle - sum property for right - angle

Since there is a right - angle (90°) and an angle of 40°, for angle \(x\), the sum of angles in that part of the intersection is 90°.
\(x + 40^{\circ}=90^{\circ}\)
\(x=90^{\circ}- 40^{\circ}\)
\(x = 50^{\circ}\)

Step2: Use angle - sum property for straight - angle

The sum of angles on a straight - line is 180°. We know one angle is 90° and \(x = 50^{\circ}\), so for angle \(y\):
\(y+90^{\circ}+x = 180^{\circ}\)
Substitute \(x = 50^{\circ}\) into the equation:
\(y+90^{\circ}+50^{\circ}=180^{\circ}\)
\(y=180^{\circ}-(90^{\circ}+50^{\circ})\)
\(y = 40^{\circ}\)

Answer:

\(x = 50^{\circ}\), \(y = 40^{\circ}\)