Question

Interpreting Parallel Lines Cut by a Transversal
Examine Carmen’s plans for rail lines at a train station.

Parallel lines k and l are crossed by transversal t. Line m crosses lines t, k, and l. The angles formed by lines k, t, and m, clockwise from top left are 2, 1, blank, blank, blank (6 x + 5) degrees; formed by lines l and t are blank, (7x minus 4) degrees, blank, blank; formed by lines l and m are 48 degrees, blank, blank, blank.

What is the measure of angle 2? es001-1.jpg =

Answer 1

Answer: 73°

Reasoning (concise):
- Let the three distinct angles at the intersection of k, t, m be a (angle 2), b (angle 1), and c (the 6x+5 angle). For three lines through a point a + b + c = 180°.
- The angle 6x + 5 (c) is the angle formed by k and t, and the given 7x − 4 at the intersection of l and t is its corresponding angle (k ∥ l). So 6x + 5 = 7x − 4 ⇒ x = 9. Thus c = 6(9)+5 = 59°.
- The 48° at the intersection of l and m corresponds to the angle formed by k and m at the intersection with k, so b = 48°.
- Then a = 180 − b − c = 180 − 48 − 59 = 73°.

So measure of angle 2 is 73°.