Question

At an airport, runways 12L and 12R are parallel and are intersected by a third runway. Mike calculated the value of x to be 115°. Which statement justifies Mike’s calculations?

a) Alternate interior angles are congruent.
b) Corresponding angles are congruent.
c) Vertical angles are congruent.
d) Supplementary angles add up to 180°.

Answer 1

The statement that justifies Mike's calculations is that supplementary angles add up to 180°.

Step-by-step explanation:

When two parallel lines are intersected by a transversal, the corresponding angles formed are congruent. In this case, runways 12L and 12R are parallel, and the third runway is the transversal. Therefore, the angle formed by runway 12L and the transversal is congruent to the angle formed by runway 12R and the transversal. Since Mike calculated the value of x to be 115°, the supplementary angle to x would be 180° - 115° = 65°, which makes it congruent to the angle formed by runway 12R and the transversal.