Question

look at this diagram: if \\( \overleftrightarrow { t v } \\) and \\( \overleftrightarrow { w y } \\) are parallel lines and \\( m \angle y x z = 111 ^ { \circ } \\), what is \\( m \angle w x u? \\)

Explanation:

Step1: Find the measure of adjacent angle to \( \angle YXZ \)

Since \( \angle YXZ\) and \( \angle WXZ\) are adjacent angles forming a linear pair (sum to \( 180^{\circ}\)), and \( m\angle YXZ = 111^{\circ}\).
Let \( m\angle WXZ=x\), then \(x + 111^{\circ}=180^{\circ}\), so \(x=180^{\circ}- 111^{\circ}=69^{\circ}\).

Step2: Use the property of parallel lines

Because \( \overleftrightarrow{TV}\parallel\overleftrightarrow{WY}\), \( \angle WXZ\) and \( \angle WXU\) are alternate - interior angles. Alternate - interior angles formed by parallel lines and a transversal are equal.

Answer:

\(69\)