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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

∠5 is congruent to ∠4.
angle 5 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 .

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

∠1 is congruent to ∠4.
angle 1 is congruent to angle 4 .
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Answer 1

To determine which angles are congruent to ∠4 in the scenario described, we can apply the properties of parallel lines cut by a transversal.

• When two parallel lines are intersected by a transversal, corresponding angles are congruent.
• Alternate interior angles are also congruent.

Given the labeling of the angles, we can analyze the angles:

• ∠4 is below line m and to the left of the transversal.
• ∠6 is directly above ∠4 and is in line with it on line n (also congruent as corresponding angles).
• ∠8 is directly opposite ∠4 and is considered alternate interior angle, thus also congruent.

So, ∠4 is congruent to:

• ∠6 (corresponding angle)
• ∠8 (alternate interior angle)

Thus, ∠4 is congruent to ∠6 and ∠8, but not to angles ∠1, ∠2, or ∠5.

The correct response from your options is: ∠5 is congruent to ∠4. ∠1, ∠5 and ∠8 are congruent to ∠4.

This option includes the congruence of ∠8, as we already identified, and is an accurate reflection of angle relationships given the properties of parallel lines and transversals.