Question

find the measure of the missing angles.

Explanation:

Step1: Use the fact that a right - angle is 90°.

We know that the angle composed of \(x\) and \(65^{\circ}\) is a right - angle. So \(x + 65^{\circ}=90^{\circ}\).

Step2: Solve for \(x\).

Subtract \(65^{\circ}\) from both sides of the equation: \(x=90^{\circ}-65^{\circ}=25^{\circ}\).

Step3: Use the fact that a straight - angle is 180°.

The angle composed of \(y\) and \(65^{\circ}\) is a straight - angle. So \(y + 65^{\circ}=180^{\circ}\).

Step4: Solve for \(y\).

Subtract \(65^{\circ}\) from both sides of the equation: \(y = 180^{\circ}-65^{\circ}=115^{\circ}\).

Answer:

\(x = 25^{\circ}\), \(y=115^{\circ}\)