Question

the figure shows a transversal that intersects two parallel lines. none of the angles are right angles. which angles are congruent to ∠3? select all that apply. ∠1 ∠2 ∠4 ∠5 ∠6 ∠7 ∠8

Explanation:

Step1: Vertical angles

Vertical angles are congruent. $\angle3$ and $\angle1$ are vertical angles, so $\angle3\cong\angle1$.

Step2: Alternate interior angles

Since the two lines are parallel and cut by a transversal, alternate - interior angles are congruent. $\angle3$ and $\angle7$ are alternate - interior angles, so $\angle3\cong\angle7$.

Step3: Corresponding angles

Corresponding angles are congruent. $\angle1$ and $\angle5$ are corresponding angles ($\angle1\cong\angle5$), and since $\angle3\cong\angle1$, then $\angle3\cong\angle5$ by transitive property.

Answer:

$\angle1$, $\angle5$, $\angle7$