Question

look at this diagram.
if qs and tv are parallel lines and m∠vur = 40°, what is m∠vuw?

Explanation:

Step1: Use the property of parallel lines and transversal

When two parallel lines \( \overleftrightarrow{QS}\) and \( \overleftrightarrow{TV}\) are cut by a transversal \( \overleftrightarrow{WP}\), the sum of the interior angles on the same side of the transversal is \(180^{\circ}\).
So, \(m\angle VUR + m\angle VUW=180^{\circ}\)

Step2: Solve for \(m\angle VUW\)

Given \(m\angle VUR = 40^{\circ}\), substitute into the equation \(m\angle VUR + m\angle VUW=180^{\circ}\)
\(m\angle VUW=180^{\circ}-m\angle VUR\)
\(m\angle VUW = 180^{\circ}- 40^{\circ}\)
\(m\angle VUW=140^{\circ}\)

Answer:

\(140^{\circ}\)