In a swimming pool, two lanes are represented by lines l and m. If a string of flags

The angles are alternate interior angles and are congruent. Therefore, the two lanes are parallel, as obtined from the alternate interior angles theorem.

Note: The diagram of the two lanes are found in the attachment below.

Step-by-step explanation:

Step 1: Stating the theorem

The alternate interior angle theorem states that, If two parallel lines are cut by a transversal, the alternate interior angles are congruent.

Step 2: Solving for size of angles

The two angles are alternate interior angles.

x = 10

Angle at L = (3x + 4)°

= 3 × 10 + 4 = 34°

Angle at M = (4x - 6)°

4 × 10 - 6 = 34°

The two angles are congruent

Since the two interior alternate angles are congruent, therefore, the two lanes must be parallel.

The best and most correct answer among the choices provided by your question is the third choice or letter C.

Angle-angle-side (AAS) is not a valid postulate or theorem of proving triangles congruent.

I hope my answer has come to your help. Thank you for posting your question here in We hope to answer more of your questions and inquiries soon. Have a nice day ahead!