Question

statements

1. ym ⊥ bw and ym ⊥ xt
2. ∠bky is a right - angle, ∠xrk is a right - angle
3. m∠bkr = 90°, m∠xrk = 90°
4. m∠bkr + m∠xrk = 90°+m∠xrk
5. m∠bkr + m∠xrk = 90° + 90°
6. m∠bkr + m∠xrk = 180
7. ∠bkr and ∠xrk are supplementary
8. bw || xt

reasons

1. given
2. definition of perpendicular lines
3. definition of right angle
4. addition property of equality
5. substitution property of equality
6. simplify
7. definition of supplementary angles

8.

Explanation:

Step1: Recall parallel - line theorem

If two lines are cut by a transversal and a pair of same - side interior angles are supplementary, then the two lines are parallel. In this case, $\angle BKY$ and $\angle XKY$ are same - side interior angles formed by the transversal $\overline{YK}$ with lines $\overline{BW}$ and $\overline{XT}$.

Answer:

If two lines are cut by a transversal and a pair of same - side interior angles are supplementary, then the two lines are parallel.