Question

select all the pairs of corresponding angles. ∠jkn and ∠mnp, ∠onk and ∠lki, ∠jki and ∠mnk, ∠onp and ∠lkn

Explanation:

Step1: Recall Corresponding Angles Definition

Corresponding angles are in the same relative position at each intersection where a transversal crosses two lines. If the two lines are parallel, corresponding angles are equal. Here, lines \( JL \) and \( MO \) are cut by transversal \( IP \).

Step2: Analyze Each Pair

• \(\angle JKN\) and \(\angle MNP\): These are in the same relative position (both below the transversal, at the intersection with the two lines), so they are corresponding angles.
• \(\angle ONK\) and \(\angle LKI\): \(\angle ONK\) is at the intersection of \( MO \) and \( IP \), and \(\angle LKI\) is at the intersection of \( JL \) and \( IP \), in the same relative position (above the transversal, on the right - hand side of the transversal for their respective lines), so they are corresponding angles.
• \(\angle JKI\) and \(\angle MNK\): \(\angle JKI\) is at the intersection of \( JL \) and \( IP \) (above \( JL \), left of \( IP \)), and \(\angle MNK\) is at the intersection of \( MO \) and \( IP \) (above \( MO \), left of \( IP \)), same relative position, so they are corresponding angles.
• \(\angle ONP\) and \(\angle LKN\): \(\angle ONP\) is at the intersection of \( MO \) and \( IP \) (below \( MO \), right of \( IP \)), and \(\angle LKN\) is at the intersection of \( JL \) and \( IP \) (below \( JL \), right of \( IP \)), same relative position, so they are corresponding angles.

Answer:

\(\angle JKN\) and \(\angle MNP\), \(\angle ONK\) and \(\angle LKI\), \(\angle JKI\) and \(\angle MNK\), \(\angle ONP\) and \(\angle LKN\)