Question

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

Explanation:

Step1: Recall the definition of a linear pair

A linear pair of angles is a pair of adjacent angles whose non - common sides are opposite rays. The sum of angles in a linear pair is \(180^{\circ}\).

Step2: Analyze each option

• Option \(\angle AEF\) and \(\angle MLG\): These angles are not adjacent.
• Option \(\angle GLH\) and \(\angle GLM\): These angles are adjacent. \(\angle GLH = 60^{\circ}\), and \(\angle GLM\) is a right - angle (since \(MJ\) is a straight line and \(\angle GLJ=120^{\circ}\), \(\angle GLM = 180^{\circ}- 60^{\circ}=120^{\circ}\) is incorrect. Wait, actually, \(\angle GLH+\angle GLM

eq180^{\circ}\) and they are not adjacent in the required way (non - common sides are not opposite rays).

• Option \(\angle KLM\) and \(\angle KLJ\):
• \(\angle KLM+\angle KLJ=(90^{\circ})+(90^{\circ}) = 180^{\circ}\) (since \(\angle GLJ = 120^{\circ}\), \(\angle LJK = 30^{\circ}\), and \(MJ\) is a straight line. \(\angle KLM\) and \(\angle KLJ\) are adjacent angles. Their non - common sides \(LM\) and \(LJ\) are opposite rays (because \(MJ\) is a straight line).
• Option \(\angle MLJ\) and \(\angle AEB\): \(\angle MLJ = 120^{\circ}\), \(\angle AEB=90^{\circ}\), \(\angle MLJ+\angle AEB

eq180^{\circ}\) and they are not adjacent.

Answer:

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