Question

find the measure of the missing angles.

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. Angle \(x\) and the \(68^{\circ}\) angle are vertical angles. So \(x = 68^{\circ}\).

Step2: Use angle - sum property

The sum of angles around a point is \(360^{\circ}\), and we also know that there is a right - angle (\(90^{\circ}\)). Let's consider the angles at the intersection. We know \(x = 68^{\circ}\), and there is a \(90^{\circ}\) angle. The sum of \(x\), \(y\), \(90^{\circ}\) and \(68^{\circ}\) is \(360^{\circ}\). But we can also use the fact that \(x\) and the non - \(y\) angle adjacent to the \(90^{\circ}\) angle are vertical. So \(y=180^{\circ}- 68^{\circ}-90^{\circ}=22^{\circ}\).

Answer:

\(x = 68^{\circ}\), \(y = 22^{\circ}\)