Question

identify all the numbered angles that are congruent to the given angle. list the numbers of any angles that are congruent to the given angle

Explanation:

Step1: Recall angle - congruence rules

When two parallel lines are cut by a transversal, vertical angles are congruent, corresponding angles are congruent, and alternate - interior and alternate - exterior angles are congruent.

Step2: Analyze vertical angles

Angle 7 is given as 96°. Angle 5 is vertical to angle 7, so $\angle5=\angle7 = 96^{\circ}$.

Step3: Analyze corresponding angles

Angle 1 is corresponding to angle 7, so $\angle1=\angle7=96^{\circ}$.

Step4: Analyze alternate - exterior angles

Angle 3 is alternate - exterior to angle 7, so $\angle3=\angle7 = 96^{\circ}$.

Answer:

1, 3, 5