Question

Two parallel lines cut by a transversal are shown. David says the value of y is 60°. Which statement supports David's thinking?

a. The angle measuring yº and the angle measuring 5xº are congruent because they are adjacent angles.
b. The angle measuring yº and the angle measuring 5xº are congruent because they are supplementary angles.
c. The angle measuring yº and the angle measuring 2(x + 6)º are congruent because they are adjacent angles.
d. The angle measuring yº and the angle measuring 2(x + 6)º are congruent because they are corresponding angles.

Answer 1

The angle measuring yº and the angle measuring 5xº are congruent and supplementary, supporting David's thinking that y is 60º.

Step-by-step explanation:

The correct statement that supports David's thinking is option b. The angle measuring yº and the angle measuring 5xº are congruent because they are supplementary angles.

In a pair of parallel lines cut by a transversal, alternate interior angles are congruent. Since the angle measuring yº and the angle measuring 5xº are alternate interior angles, they are congruent. Furthermore, the sum of the measures of the two angles is 180º, making them supplementary angles.

Therefore, David is correct in stating that the value of y is 60º because the angle measuring yº and the angle measuring 5xº are congruent and supplementary.