Question

which angle pair is a linear pair? ∠mlj and ∠aeb ∠glh and ∠glm ∠klm and ∠klj ∠aef and ∠mlg

Explanation:

Step1: Recall the definition of a linear pair

A linear pair of angles is formed when two adjacent angles form a straight line (sum to \(180^{\circ}\)).

Step2: Analyze \(\angle KLM\) and \(\angle KLJ\)

Looking at the first diagram, \(\angle KLM\) and \(\angle KLJ\) are adjacent angles. They share a common side \(LK\) and their non - common sides \(LM\) and \(LJ\) form a straight line \(MJ\). So, \(\angle KLM+\angle KLJ = 180^{\circ}\) (since \(MJ\) is a straight line).

Step3: Analyze \(\angle MLJ\) and \(\angle AEB\)

\(\angle MLJ\) is from the first diagram and \(\angle AEB\) is from the second diagram. They are not adjacent and do not form a straight line together.

Step4: Analyze \(\angle GLH\) and \(\angle GLM\)

\(\angle GLH+\angle GLM=60^{\circ}+(180 - 60)^{\circ}=180^{\circ}\), but they are not adjacent (they have no common side in the way required for a linear pair as per the angle - pair definition in the context of the problem's diagrams).

Step5: Analyze \(\angle AEF\) and \(\angle MLG\)

\(\angle AEF\) is from the second diagram and \(\angle MLG\) is from the first diagram. They are not adjacent and do not form a straight line together.

Answer:

\(\angle KLM\) and \(\angle KLJ\)