Question

select all of the angles that are congruent to \\( \angle 5 \\).
\\( \square \angle 1 \\)
\\( \square \angle 2 \\)
\\( \square \angle 3 \\)
\\( \square \angle 4 \\)
\\( \square \angle 7 \\)
\\( \square \angle 8 \\)

Explanation:

Step1: Identify vertical angles

Vertical angles are congruent. $\angle5$ and $\angle7$ are vertical angles, so $\angle5\cong\angle7$.

Step2: Identify alternate - interior angles

Since lines $\ell$ and $m$ are parallel (assumed from the transversal - cut - parallel - lines context), alternate - interior angles are congruent. $\angle5$ and $\angle3$ are alternate - interior angles, so $\angle5\cong\angle3$.

Step3: Use the property of vertical angles and parallel lines for $\angle2$

$\angle3$ and $\angle2$ are vertical angles ($\angle3\cong\angle2$). Since $\angle5\cong\angle3$, by transitivity, $\angle5\cong\angle2$.

Answer:

$\angle2$, $\angle3$, $\angle7$