Question

if m∠8 = 32° select all other angles that are also 32°

Explanation:

Step1: Identify vertical - angle relationship

Vertical angles are equal. $\angle1$ and $\angle3$ are vertical angles, $\angle2$ and $\angle4$ are vertical angles, $\angle5$ and $\angle7$ are vertical angles, $\angle6$ and $\angle8$ are vertical angles. Since $\angle8 = 32^{\circ}$, $\angle6=32^{\circ}$.

Step2: Identify corresponding - angle relationship

Corresponding angles are equal when two parallel lines are cut by a transversal. $\angle1$ and $\angle5$ are corresponding angles, $\angle2$ and $\angle6$ are corresponding angles, $\angle3$ and $\angle7$ are corresponding angles, $\angle4$ and $\angle8$ are corresponding angles. Since $\angle8 = 32^{\circ}$, and $\angle1$ and $\angle8$ are alternate - exterior angles (alternate - exterior angles are equal when two parallel lines are cut by a transversal), $\angle1 = 32^{\circ}$.

Answer:

$\angle1, \angle6$