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

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

Step2: Analyze \(\angle MLJ\) and \(\angle AEB\)

\(\angle MLJ = 90^{\circ}+ 50^{\circ}=140^{\circ}\), \(\angle AEB = 90^{\circ}\). They are non - adjacent but \(140^{\circ}+90^{\circ}
eq90^{\circ}\) and \(140^{\circ}+90^{\circ}
eq180^{\circ}\)

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

They are adjacent angles.

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

\(\angle KLJ = 50^{\circ}\), \(\angle AEB = 90^{\circ}\), \(50^{\circ}+90^{\circ}=140^{\circ}
eq90^{\circ}\) and \(50^{\circ}+90^{\circ}
eq180^{\circ}\), but they are non - adjacent. Wait, no:

• \(\angle KLJ = 50^{\circ}\), \(\angle AEB=90^{\circ}\). But let's check again:
• For \(\angle MLJ\) and \(\angle AEB\):

\(\angle MLJ = 180^{\circ}- 40^{\circ}=140^{\circ}\) (since \(\angle GLH = 60^{\circ}\), \(\angle MLG = 90^{\circ}-60^{\circ} = 30^{\circ}\), \(\angle MLJ=30^{\circ}+ 110^{\circ}\)? No, wait, \(\angle MLJ\): \(\angle GLH = 60^{\circ}\), \(\angle MLH = 90^{\circ}\), so \(\angle MLG=90^{\circ}-60^{\circ}=30^{\circ}\), and \(\angle GLJ = 180^{\circ}-50^{\circ}=130^{\circ}\), no, wait, original: \(\angle GLH = 60^{\circ}\), \(MH\perp GJ\), so \(\angle MLH = 90^{\circ}\), \(\angle MLG=90^{\circ}-60^{\circ} = 30^{\circ}\), \(\angle GLJ=180^{\circ}-50^{\circ}=130^{\circ}\), \(\angle MLJ=\angle MLG+\angle GLJ\) no, wrong. Wait, \(\angle MLJ\): since \(MH\perp GJ\) (assuming \(MH\) is vertical and \(GJ\) is a line), \(\angle MLH = 90^{\circ}\), \(\angle LJH = 50^{\circ}\), \(\angle MLJ=90^{\circ}+50^{\circ}=140^{\circ}\), \(\angle AEB = 90^{\circ}\). They are non - adjacent, \(140 + 90
eq90\) and \(140+90
eq180\)

Answer:

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