Question

m∠pvs = □°

Explanation:

Step1: Identify the relationship

Since lines \( RS \) and \( TU \) are parallel (as they are both horizontal and cut by a transversal \( PQ \)), the corresponding angles \( \angle PVS \) and \( \angle PWU \) (or the given angles \( (143 - 5x)^\circ \) and \( (11x - 17)^\circ \)) are equal because they are corresponding angles. So we set up the equation:
\( 143 - 5x = 11x - 17 \)

Step2: Solve for \( x \)

Add \( 5x \) to both sides:
\( 143 = 16x - 17 \)
Add \( 17 \) to both sides:
\( 160 = 16x \)
Divide both sides by \( 16 \):
\( x = 10 \)

Step3: Find \( m\angle PVS \)

Substitute \( x = 10 \) into \( (143 - 5x)^\circ \):
\( 143 - 5(10) = 143 - 50 = 93 \)

Answer:

\( 93 \)