Question

select all the pairs of consecutive interior angles.
∠kjh and ∠nmj ∠lmj and ∠ijh
∠nmj and ∠kjm ∠ijm and ∠lmj

Explanation:

Step1: Recall Consecutive Interior Angles Definition

Consecutive interior angles are two angles that lie between two lines (the "interior") and on the same side of the transversal. The two lines are cut by a transversal, so we need to identify which pairs of angles satisfy this: between the two non - transversal lines, on the same side of the transversal.

Step2: Analyze Each Option

• For \(\angle KJH\) and \(\angle NMJ\): The two lines are \(LN\) and \(IK\), and the transversal is \(OH\). \(\angle KJH\) and \(\angle NMJ\) are between \(LN\) and \(IK\) (interior) and on the same side of \(OH\) (transversal), so they are consecutive interior angles.
• For \(\angle LMJ\) and \(\angle IJH\): The two lines are \(LN\) and \(IK\), transversal is \(OH\). \(\angle LMJ\) and \(\angle IJH\) are between \(LN\) and \(IK\) (interior) and on the same side of \(OH\) (transversal), so they are consecutive interior angles.
• For \(\angle NMJ\) and \(\angle KJM\): These angles are not between the two lines \(LN\) and \(IK\) in the correct way for consecutive interior angles. \(\angle KJM\) and \(\angle NMJ\) do not lie on the same side of the transversal in the context of the two lines \(LN\) and \(IK\).
• For \(\angle IJM\) and \(\angle LMJ\): These angles are not between the two lines \(LN\) and \(IK\) in the correct way for consecutive interior angles. They do not satisfy the "between the two lines" and "same side of transversal" conditions.

Answer:

\(\angle KJH\) and \(\angle NMJ\), \(\angle LMJ\) and \(\angle IJH\)