Question

what is an angle that is adjacent to ∠aeb?

Explanation:

Step1: Recall adjacent angle definition

Adjacent angles share a common side and vertex, and their non - common sides form a linear pair (or are adjacent rays). For $\angle AEB$, the vertex is $E$, and one side is $EB$.

Step2: Identify adjacent angle

Looking at the diagram, $\angle DEB$ (or $\angle HEB$ or $\angle CEB$ can be considered, but let's check the common side. $\angle AEB$ and $\angle DEB$ share the side $EB$ and vertex $E$, and their non - common sides $EA$ and $ED$ (or $EH$) are adjacent rays (lie on a straight line with $EB$? Wait, actually, $\angle AEB$ and $\angle CEB$: Wait, no, let's re - examine. Wait, the lines: $AB$ (with $A$ and $B$), $CD$ (with $C$ and $F$? Wait, no, the diagram has lines: one vertical line $HB$ with points $H$, $D$, $E$, $B$; and two slant lines: one with $C$, $E$, $A$ and another with $G$, $D$, $F$. So $\angle AEB$ has vertex $E$, sides $EA$ and $EB$. An adjacent angle should share a side (either $EA$ or $EB$) and vertex $E$. So $\angle DEB$ (sharing $EB$ and vertex $E$, with side $ED$) or $\angle CEB$? Wait, no, $CE$ and $EA$ are on the same line? Wait, $C - E - A$: so $CE$ and $EA$ are a straight line. So $\angle AEB$ and $\angle DEB$: $EB$ is common, $EA$ and $ED$: $ED$ is on the vertical line. Wait, maybe $\angle DEB$ is adjacent. But the given answer was $\angle CEB$, but actually, let's correct. Wait, no, $C - E - A$ is a straight line, so $\angle AEB$ and $\angle CEB$: wait, $CE$ and $EA$ are a straight line, so $\angle CEB$ and $\angle AEB$: do they share a common side? $\angle AEB$: sides $EA$, $EB$; $\angle CEB$: sides $EC$, $EB$. So they share $EB$ and vertex $E$, and $EC$ and $EA$ are a straight line (since $C - E - A$), so they are adjacent (supplementary and share a side and vertex). Alternatively, $\angle DEB$: $ED$ and $EB$ (vertical line), $EA$ and $ED$: not a straight line? Wait, maybe the correct adjacent angle is $\angle DEB$ or $\angle HEB$ or $\angle CEB$. But let's go with the diagram. The vertical line is $H - D - E - B$, and the slant line is $C - E - A$. So $\angle AEB$ (at $E$, between $EA$ and $EB$) and $\angle DEB$ (at $E$, between $ED$ and $EB$) share $EB$ and vertex $E$, and $EA$ and $ED$: no, $ED$ is vertical, $EA$ is slant. Wait, maybe I made a mistake. Wait, the other slant line is $G - D - F$. So at point $E$, we have three lines: $EB$ (vertical down), $EA$ (slant down - right), and $EC$ (slant up - left). So $\angle AEB$ is between $EA$ and $EB$. An adjacent angle would be between $EB$ and $EC$ (i.e., $\angle CEB$) because they share $EB$ and vertex $E$, and $EC$ and $EA$ are a straight line (since $C - E - A$). So $\angle CEB$ is adjacent to $\angle AEB$.

Answer:

$\angle CEB$ (or $\angle DEB$, $\angle HEB$ are also possible, but based on the diagram and the given box, $\angle CEB$ is a valid adjacent angle)