Question

r s t u q m∠pvs = °

Explanation:

Step1: Identify the relationship

Since \( RS \parallel TU \) and \( PQ \) is a transversal, \( \angle PVS \) and \( \angle PWU \) (or the angle \( (11x - 17)^\circ \)) are corresponding angles, so they are equal. Wait, actually, looking at the diagram, \( \angle PVS=(143 - 5x)^\circ \) and the angle \( (11x - 17)^\circ \) are equal because \( RS \parallel TU \) and \( PQ \) is a transversal, so corresponding angles are equal. 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:
\( 143 + 17 = 16x \)
\( 160 = 16x \)
Divide both sides by 16:
\( x = \frac{160}{16}=10 \)

Step3: Find \( m\angle PVS \)

Substitute \( x = 10 \) into \( (143 - 5x)^\circ \):
\( 143-5\times10 = 143 - 50 = 93 \)

Answer:

\( 93 \)