Question

classify the angle pair \\( \angle mlj \\) and \\( \angle aeb \\).
nonadjacent and supplementary
a linear pair
nonadjacent and neither complementary nor
supplementary
nonadjacent and complementary

Explanation:

Step1: Find the measure of \(\angle MLJ\)

Using the fact that the sum of angles around a point \(L\) is \(180^{\circ}\). Given \(\angle GLH = 60^{\circ}\), then \(\angle MLJ=180^{\circ}- 60^{\circ}-90^{\circ}=30^{\circ}\) (since \(\angle MLG = 90^{\circ}\) as it is a right - angle formed by the perpendicular lines \(MH\) and \(GJ\)).

Step2: Find the measure of \(\angle AEB\)

Since \(AE\perp BD\) (perpendicular lines), \(\angle AEB = 60^{\circ}\) (vertically opposite angles to the non - right angle in the first figure's non - right - angle at \(L\) - like structure. In the second figure, the angles around \(E\): \(\angle AEB\) and the angle adjacent to it (which is \(30^{\circ}\) from the perpendicular \(AE\) and the line \(CF\) relation similar to the first figure's angle relations).

Step3: Check the sum and adjacency

The sum \(\angle MLJ+\angle AEB=30^{\circ}+60^{\circ} = 90^{\circ}\). Also, the two angles \(\angle MLJ\) and \(\angle AEB\) are not adjacent (they are in different figures, no common side and no common vertex).

Answer:

Nonadjacent and complementary