To solve the problem, we need to identify the alternate interior angles formed by the transversal line $ KN $ intersecting the parallel lines $ JL $ and $ MO $. Let's go through the solution step by step.
Step 1: Understand the Definition of Alternate Interior Angles
Alternate interior angles are the pairs of angles that:
- Are on opposite sides of the transversal.
- Are between the two parallel lines.
Step 2: Identify the Transversal and Parallel Lines
- The transversal is the line $ KN $.
- The parallel lines are $ JL $ and $ MO $.
Step 3: Locate the Angles Formed by the Transversal
The transversal $ KN $ intersects the parallel lines $ JL $ and $ MO $, creating several angles. We need to focus on the angles that are:
1. On opposite sides of the transversal $ KN $.
2. Between the parallel lines $ JL $ and $ MO $.
Step 4: Analyze the Given Angle Pairs
We are given four pairs of angles to consider:
1. \( \angle JKN \) and \( \angle ONK \)
2. \( \angle LKI \) and \( \angle MNP \)
3. \( \angle JKN \) and \( \angle LKI \)
4. \( \angle MNP \) and \( \angle LKN \)
#### Pair 1: \( \angle JKN \) and \( \angle ONK \)
- \( \angle JKN \) is on one side of the transversal $ KN $.
- \( \angle ONK \) is on the other side of the transversal $ KN $.
- Both angles are between the parallel lines $ JL $ and $ MO $.
- Therefore, \( \angle JKN \) and \( \angle ONK \) are alternate interior angles.
#### Pair 2: \( \angle LKI \) and \( \angle MNP \)
- \( \angle LKI \) is on one side of the transversal $ KN $.
- \( \angle MNP \) is on the other side of the transversal $ KN $.
- However, \( \angle LKI \) is not between the parallel lines $ JL $ and $ MO $; it is outside the parallel lines.
- Therefore, \( \angle LKI \) and \( \angle MNP \) are not alternate interior angles.
#### Pair 3: \( \angle JKN \) and \( \angle LKI \)
- \( \angle JKN \) is on one side of the transversal $ KN $.
- \( \angle LKI \) is on the same side of the transversal $ KN $.
- Since they are on the same side, they cannot be alternate interior angles.
- Therefore, \( \angle JKN \) and \( \angle LKI \) are not alternate interior angles.
#### Pair 4: \( \angle MNP \) and \( \angle LKN \)
- \( \angle MNP \) is on one side of the transversal $ KN $.
- \( \angle LKN \) is on the other side of the transversal $ KN $.
- However, \( \angle LKN \) is not between the parallel lines $ JL $ and $ MO $; it is outside the parallel lines.
- Therefore, \( \angle MNP \) and \( \angle LKN \) are not alternate interior angles.
Step 5: Conclusion
The only pair of angles that satisfy the definition of alternate interior angles is:
\[ \angle JKN \text{ and } \angle ONK \]
Final Answer:
\[
\boxed{\angle JKN \text{ and } \angle ONK}
\]
Parent Tip: Review the logic above to help your child master the concept of parallel lines and transversals practice worksheet.
