Angles and Parallel Lines Quick Check

Question

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Question
Use the image to answer the question.

A diagram shows two horizontal parallel lines labeled m and n. They are intersected by an upward diagonal line that is labeled transversal. All three lines have arrows at both ends. The eight angles formed by the transversal are labeled 1 to 8. The angles formed by the intersection of the transversal and m are labeled 1, 2 above line m, and 3, 4 below. The angles formed by the intersection of the transversal and n is labeled 5, 6, above line n, and 7, 8 below. The text at the bottom reads lines m and n are parallel lines.

Which angles are congruent to ∠4 ?

(1 point)
Responses

∠2 is congruent to ∠4.
angle 2 is congruent to angle 4 .

∠1, ∠5 and ∠8 are congruent to ∠4.
angle 1 , angle 5 and angle 8 are congruent to angle 4 .

∠5 is congruent to ∠4.
angle 5 is congruent to angle 4 .

∠1 is congruent to ∠4.

Answer 1

When two parallel lines are intersected by a transversal, certain angle relationships occur.

In your scenario, the angles formed can be classified as follows:

• Corresponding Angles: Angles that are in the same relative position at each intersection.
• Alternate Interior Angles: Angles that are on opposite sides of the transversal and inside the parallel lines.
• Alternate Exterior Angles: Angles that are on opposite sides of the transversal and outside the parallel lines.

Given that angles 4 is below line m and adjacent to that same transversal, we can identify its congruent angles:

1. ∠4 and ∠2: These are alternate interior angles.
2. ∠4 and ∠6: These are corresponding angles.
3. ∠4 and ∠8: These are alternate exterior angles.

Since angle 4 has congruences with:

• Angle 2 (alternate interior)
• Angle 6 (corresponding)
• Angle 8 (alternate exterior)

Thus, the angles congruent to ∠4 are ∠2, ∠6, and ∠8.

Therefore, the correct response is: ∠1, ∠5, and ∠8 are congruent to ∠4.

Note: Angles 1 and 5 are not congruent to angle 4.

In this case, the correct response among the provided ones would be: ∠5 is congruent to ∠4. (This is incorrect, but no other set matches).

If this is a select-all question of congruence, the best fit from the choices is that ∠2 is congruent to ∠4. If you meant to only identify one angle, choose this.