Question

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

Explanation:

Step1: Recall definitions

Adjacent angles share a common side and vertex. Complementary angles sum to \(90^{\circ}\), supplementary angles sum to \(180^{\circ}\).

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

\(\angle MLK\) and \(\angle KLJ\) are adjacent (share side \(LK\) and vertex \(L\)) and supplementary (\(\angle MLK+\angle KLJ = 180^{\circ}\) as they form a linear - pair).

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

\(\angle MLJ\) is \(80^{\circ}+32^{\circ}=112^{\circ}\), \(\angle AEB = 90^{\circ}\). They are non - adjacent (no common side or vertex) and \(\angle MLJ+\angle AEB=112^{\circ}+90^{\circ}
eq90^{\circ}\) and \(
eq180^{\circ}\).

Step4: Analyze \(\angle KIJ\) and \(\angle AEB\)

\(\angle KIJ = 32^{\circ}\), \(\angle AEB=90^{\circ}\). They are non - adjacent and \(\angle KIJ+\angle AEB = 32^{\circ}+90^{\circ}
eq90^{\circ}\) and \(
eq180^{\circ}\). But \(\angle MLJ\) is the angle formed by \(\angle HLG = 80^{\circ}\) (vertical angle property) and \(\angle JLK = 32^{\circ}\).

Step5: Analyze \(\angle CEB\) and \(\angle BEA\)

\(\angle CEB\) and \(\angle BEA\) are adjacent (share side \(BE\) and vertex \(E\)) and \(\angle CEB+\angle BEA = 90^{\circ}\) (complementary as \(\angle DEB = 90^{\circ}\) and \(\angle CEB\) and \(\angle DEB\) - related by vertical angles etc. conceptually wrong for non - adjacent check, but actual check: \(\angle MLJ\) and \(\angle AEB\) is the pair.

Answer:

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