Answer:
The order of the start of the proof seems fine; we're to choose the next steps I guess.
segment UV is parallel to segment WZ Given
Points S, Q, R, and T all lie on the same line. Given
m∠SQT = 180° Definition of a Straight Angle
m∠SQV + m∠VQT = m∠SQT Angle Addition Postulate
m∠SQV + m∠VQT = 180° Substitution Property of Equality
That's all valid up to here. It seems to me sort of the hard way to get to linear supplements but here we are.
ZRS is mentioned in the rest of the lines; let's find the one that comes first.
III m∠VQT + m∠ZRS = 180° Same-Side Interior Angles Theorem
Now we have two things equal to 180 degrees, so they're equal to each other.
II m∠SQV + m∠VQT = m∠VQT + m∠ZRS Substitution Property of Equality
Now comes
I m∠SQV + m∠VQT − m∠VQT = m∠VQT + m∠ZRS − m∠VQT
m∠SQV = m∠ZRS Subtraction Property of Equality
And we conclude,
∠SQV ≅ ∠ZRS Definition of Congruency
