Answer:
Explanation:
To prove that line j is parallel to line k, we need to show that the corresponding angles formed by these lines are congruent. In this case, we are given that angle 4 and angle 7 are supplementary.
1. Supplementary angles: When two angles are supplementary, the sum of their measures is 180 degrees.
2. Angle 4 and angle 7: Since angle 4 and angle 7 are supplementary, we can write their relationship as:
angle 4 + angle 7 = 180 degrees.
3. Corresponding angles: When two lines are parallel, the corresponding angles formed by a transversal are congruent.
4. Proving line j || line k: To prove that line j is parallel to line k, we need to show that the corresponding angles formed by these lines are congruent. Let's assume that angle 4 is a corresponding angle to angle 7.
5. Angle 4 and angle 7 congruence: From step 2, we know that angle 4 + angle 7 = 180 degrees. Since angle 4 and angle 7 are supplementary, we can conclude that angle 4 = angle 7.
6. Corresponding angles are congruent: Since angle 4 is congruent to angle 7, this means that the corresponding angles formed by line j and line k are congruent.
7. Line j || line k: Therefore, based on the congruence of corresponding angles, we can conclude that line j is parallel to line k.
In conclusion, by using the fact that angle 4 and angle 7 are supplementary, we have proven that line j is parallel to line k.