Observe the figure.
After the given statements as:
Statement 1: [tex]UV\parallel WZ[/tex]
Statement 2: Points S,Q,R and T are all lie on the same plane.
Statement 3: [tex]m \angle SQT = 180^\circ[/tex]
Statement 4: [tex]m \angle SQV + m \angle VQT = m \angle SQT[/tex]
Statement 5: [tex]m \angle SQV + m \angle VQT =180^\circ[/tex]
Now, the next statement is as:
Statement 6: [tex]m \angle VQT + m \angle ZRS =180^\circ[/tex] which is statement III.
(Same side interior angles theorem)
Statement 7: [tex]m \angle SQV + m \angle VQT=m \angle VQT + m \angle ZRS[/tex] which is statement II.
(Substitution property of equality)
Statement 8: [tex]m \angle SQV + m \angle VQT-m \angle VQT=m \angle VQT + m \angle ZRS-m \angle VQT[/tex]
[tex]m \angle SQV = m \angle ZRS[/tex]which is statement I.
(Subtraction property of equality)
So, the correct order of the given reasons to complete the proof is III, II, I.
Therefore, Option 4 is the correct answer.
