Question

complete the proof that m∠rw v + m∠st y = 180°. statement reason 1 (overleftrightarrow{ik}paralleloverleftrightarrow{su}) 2 (overleftrightarrow{ik}paralleloverleftrightarrow{vx}) 3 ∠rw v≅∠ijr 4 m∠ijr + m∠st y = 180° 5 m∠rw v + m∠st y = 180°

Explanation:

Step1: Given

Parallel - line notation given.

Step2: Given

Another parallel - line notation given.

Step3: Corresponding angles postulate

Since \(IK\parallel VX\), corresponding angles are congruent.

Step4: Same - side interior angles theorem

Since \(IK\parallel SU\), same - side interior angles are supplementary.

Step5: Substitution property

Because \(\angle RWV\cong\angle IJR\), we substitute \(\angle IJR\) with \(\angle RWV\).

Answer:

1. Given
2. Given
3. Corresponding angles postulate
4. Same - side interior angles theorem
5. Substitution property