In a swimming pool, two lanes are represented by lines l and m. If a string of flags strung across the lanes is represented by transversal t, and x = 10, show that the lanes are parallel.

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.

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