Question

If ∠1||∠l, ∠m∠1 = 135°, ∠m∠2 = 55°, and ∠m∠3 = 45°, list all other parallel lines. Justify your answers.

A) ∠1 and ∠2 are parallel, and ∠1 and ∠3 are parallel.
B) ∠1 and ∠2 are parallel, and ∠2 and ∠3 are parallel.
C) ∠1 and ∠3 are parallel, and ∠2 and ∠3 are parallel.
D) None of the angles are parallel, as parallel lines have equal angles.

Answer 1

The correct answer is A) ∠1 and ∠2 are parallel, and ∠1 and ∠3 are parallel.

Step-by-step explanation:

The correct answer is A) ∠1 and ∠2 are parallel, and ∠1 and ∠3 are parallel.

To justify this answer, we need to understand the properties of parallel lines. When a transversal intersects two parallel lines, the corresponding angles are congruent. Therefore, if ∠1 is parallel to ∠l, and ∠m∠1 = 135°, then ∠m∠l is also 135°. Similarly, if ∠1 is parallel to ∠l, and ∠m∠3 = 45°, then ∠m∠l is also 45°. Therefore, ∠m∠2 and ∠m∠3 cannot be parallel to each other.