@pinkfloyd @taskmasters im stuck one question? ? / use the figure to answer the question that follows: segments uv and wz are parallel with line st intersecting both at points q and r respectively when written in the correct order, the two-column proof below describes the statements and reasons for proving that corresponding angles are congruent: statements reasons segment uv is parallel to segment wz given points s, q, r, and t all lie on the same line. given i m∠sqt = 180° definition of a straight angle ii m∠sqv + m∠vqt = 180° substitution property of equality iii m∠sqv + m∠vqt = m∠sqt angle addition postulate m∠vqt + m∠zrs = 180° same-side interior angles theorem m∠sqv + m∠vqt = m∠vqt + m∠zrs substitution property of equality m∠sqv + m∠vqt − m∠vqt = m∠vqt + m∠zrs − m∠vqt m∠sqv = m∠zrs subtraction property of equality ∠sqv ≅ ∠zrs definition of congruency which is the most logical order of statements and reasons i, ii, and iii to complete the proof?

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Step-by-step explanation:

Given that Segments UV and WZ are parallel with line ST intersecting both at points Q and R respectively.We prove that corresponding angles are congruent as follows:               Statements                                                            Reasons

segment UV is parallel to segment WZ                                 Given                    Points S, Q, R, and T all lie on the same line.                       GivenII.)  m∠SQT = 180°                                                     Definition of a Straight AngleIII.) m∠SQV + m∠VQT = m∠SQT                               Angle Addition Postulate I.)   m∠SQV + m∠VQT = 180°                                   Substitution Property of Equalitym∠VQT + m∠ZRS = 180°                                      Same-Side Interior Angles Theorem

m∠SQV + m∠VQT = m∠VQT + m∠ZRS                Substitution Property of Equality

m∠SQV + m∠VQT − m∠VQT = m∠VQT + m∠ZRS − m∠VQT

m∠SQV = m∠ZRS                                                  Subtraction Property of Equality

∠SQV ≅ ∠ZRS                                                        Definition of Congruency Therefore, the most logical order of statements and reasons I, II, and III to complete the proof is ||, |||, |. I hope this helped.

the answer for this question is 38