Question

if m∠fhc = 71°, then what is m∠dhe?
answer attempt 2 out of 2
m∠dhe = °
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Explanation:

Step1: Identify Vertical Angles

Vertical angles are equal. $\angle FHC$ and $\angle DHE$ are vertical angles? Wait, no, wait. Wait, $\angle FHC$ and $\angle DHE$: Wait, actually, $\angle FHC$ and $\angle DHE$—wait, looking at the diagram, lines $AB$ and $EF$ intersect with line $CD$. Wait, $\angle FHC$ and $\angle DHE$: Wait, no, maybe $\angle FHC$ and $\angle DHE$ are vertical angles? Wait, no, let's check the diagram. Wait, $\angle FHC$ and $\angle DHE$—wait, actually, $\angle FHC$ and $\angle DHE$: Wait, no, maybe I made a mistake. Wait, $\angle FHC$ and $\angle DHE$: Wait, the lines: $CD$ is a straight line, $EF$ is a straight line? Wait, no, $AB$ is horizontal, $CD$ is vertical (or slanting), and $EF$ is another line. Wait, actually, $\angle FHC$ and $\angle DHE$ are vertical angles? Wait, no, vertical angles are formed by two intersecting lines. So lines $CD$ and $EF$ intersect at $H$, so $\angle FHC$ and $\angle DHE$: Wait, $\angle FHC$ and $\angle DHE$—wait, $\angle FHC$ and $\angle DHE$: Wait, maybe $\angle FHC$ and $\angle DHE$ are vertical angles? Wait, no, let's see: $\angle FHC$ and $\angle DHE$: If we look at the intersection of $CD$ and $EF$ at $H$, then $\angle FHC$ and $\angle DHE$ are vertical angles? Wait, no, vertical angles are opposite each other when two lines intersect. So when two lines intersect, the opposite angles are vertical angles and are equal. So if $\angle FHC$ is 71 degrees, then $\angle DHE$ should be equal to $\angle FHC$? Wait, no, wait, maybe I got the angles wrong. Wait, no, maybe $\angle FHC$ and $\angle DHE$ are vertical angles. Wait, let's re-examine the diagram. The points: $C$, $G$, $H$, $D$ are on a straight line (line $CD$). $E$, $H$, $F$ are on a straight line (line $EF$). So lines $CD$ and $EF$ intersect at $H$. Therefore, $\angle FHC$ and $\angle DHE$ are vertical angles. Vertical angles are equal. So if $m\angle FHC = 71^\circ$, then $m\angle DHE = 71^\circ$? Wait, no, wait, maybe I mixed up the angles. Wait, no, vertical angles are equal. So if two lines intersect, the vertical angles are equal. So lines $CD$ and $EF$ intersect at $H$, so $\angle FHC$ and $\angle DHE$ are vertical angles. Therefore, they are equal. So $m\angle DHE = 71^\circ$.

Step2: Confirm Vertical Angles

Since $\angle FHC$ and $\angle DHE$ are vertical angles (formed by the intersection of lines $CD$ and $EF$ at point $H$), their measures are equal. Given $m\angle FHC = 71^\circ$, we conclude $m\angle DHE = 71^\circ$.

Answer:

$71$