Question

which angle pair is nonadjacent and neither complementary nor supplementary?
∠mlj and ∠aeb
∠ceb and ∠bea
∠klj and ∠aeb
∠mlk and ∠klj

Explanation:

Step1: Analyze \(\angle MLJ\) and \(\angle AEB\)

\(\angle MLJ = 180^{\circ}- 30^{\circ}=150^{\circ}\). \(\angle AEB = 90^{\circ}\). They are non - adjacent. \(150^{\circ}+90^{\circ}
eq90^{\circ}\) and \(150^{\circ}+90^{\circ}
eq180^{\circ}\), so they are neither complementary nor supplementary.

Step2: Analyze \(\angle CEB\) and \(\angle BEA\)

\(\angle CEB+\angle BEA = 180^{\circ}\) (linear pair), so they are supplementary.

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

\(\angle KLJ = 30^{\circ}\), \(\angle AEB = 90^{\circ}\). \(30^{\circ}+90^{\circ}=120^{\circ}
eq90^{\circ}\) and \(30^{\circ}+90^{\circ}
eq180^{\circ}\), but they are adjacent.

Step4: Analyze \(\angle MLK\) and \(\angle KLJ\)

\(\angle MLK+\angle KLJ = 180^{\circ}\) (linear pair), so they are supplementary.

Answer:

\(\angle MLJ\) and \(\angle AEB\)