Question

find the measure of the indicated angle that makes lines u and v parallel.
12)
13)

Explanation:

Step1: Use the property of alternate interior angles

When two parallel lines are cut by a transversal, alternate interior angles are equal. For problem 12, if lines \(u\) and \(v\) are parallel, the angle \(x\) and the \(104^{\circ}\) angle are supplementary (consecutive interior angles). But wait, no, actually, if we consider the adjacent angle to \(104^{\circ}\) (which is \(180 - 104=76^{\circ}\)), and using the alternate - interior angles property. So \(x = 76^{\circ}\)

Step2: Use the property of corresponding angles

For problem 13, when lines \(u\) and \(v\) are parallel, corresponding angles are equal. The angle \(x\) and the \(89^{\circ}\) angle are corresponding angles. So \(x = 89^{\circ}\)

Answer:

1. \(76^{\circ}\)
2. \(89^{\circ}\)