Question

su || vx, complete the proof that m∠twv + m∠stw = 180°.
diagram showing lines su, vx, and ry with points t, w

statement	reason
2. $\angle twv \cong \angle rts$	reason to complete
3. $m\angle rts + m\angle stw = 180^\circ$	angles forming a linear pair sum to $180^\circ$
4. $m\angle twv + m\angle stw = 180^\circ$	substitution

Explanation:

Step1: Identify the angle relationship

Since \( \overleftrightarrow{SU} \parallel \overleftrightarrow{VX} \) and \( \overleftrightarrow{RY} \) is a transversal, \( \angle TWV \) and \( \angle RTS \) are corresponding angles.

Step2: Recall the corresponding angles postulate

Corresponding angles are congruent when two parallel lines are cut by a transversal. So the reason for \( \angle TWV \cong \angle RTS \) is "Corresponding Angles Postulate (or Corresponding Angles are Congruent when lines are parallel)".

Answer:

Corresponding Angles Postulate (or Corresponding Angles are Congruent when two parallel lines are cut by a transversal)