Question

which angle pair is nonadjacent and neither complementary nor supplementary?

∠mlk and ∠klj

∠klj and ∠aeb

∠mlj and ∠aeb

∠ceb and ∠dea

Explanation:

Step1: Analyze adjacent angles

Adjacent angles share a common side and a common vertex. $\angle MLK$ and $\angle KLJ$ are adjacent (share side $LK$), so this pair is not non - adjacent.

Step2: Analyze complementary and supplementary angles

Complementary angles sum to $90^{\circ}$, and supplementary angles sum to $180^{\circ}$.

• $\angle CEH$ and $\angle DEA$ are vertical angles (equal), not complementary or supplementary, but they are adjacent (share vertex $E$).
• $\angle MLJ$ and $\angle AEB$: $\angle MLJ = 60^{\circ}+60^{\circ}=120^{\circ}$, $\angle AEB = 60^{\circ}$. They are non - adjacent (no common side or vertex) and $120^{\circ}+60^{\circ}

eq90^{\circ}$ and $120^{\circ}+60^{\circ}
eq180^{\circ}$.

• $\angle KLJ$ and $\angle AEB$: $\angle KLJ = 60^{\circ}$, $\angle AEB = 60^{\circ}$. They are non - adjacent but $\angle KLJ+\angle AEB = 120^{\circ}

eq90^{\circ}$ and $
eq180^{\circ}$, but we need to check non - adjacent first. Wait, re - check:
$\angle KLJ$ and $\angle AEB$:
$\angle KLJ$ is in the left figure, $\angle AEB$ is in the right figure. They have no common side or vertex (non - adjacent). $\angle KLJ = 60^{\circ}$, $\angle AEB=60^{\circ}$, sum is $120^{\circ}
eq90^{\circ}$ and $
eq180^{\circ}$. But wait, $\angle MLJ$: $\angle MLJ=120^{\circ}$ (since $\angle GLH = 60^{\circ}$, $\angle MLJ = 180^{\circ}- 60^{\circ}=120^{\circ}$ if we consider the straight line $GH$). $\angle AEB = 60^{\circ}$. They are non - adjacent (different figures, no common side/vertex), and $120^{\circ}+60^{\circ}
eq90^{\circ}$ and $120^{\circ}+60^{\circ}
eq180^{\circ}$.

Answer:

$\angle MLJ$ and $\angle AEB$