Question clockw

4.1 Lines, Angles, and Triangles - Angle relationships (parallel lines)
0:00

  • Clockwise from top left, the 3 lines are labeled n, r, and s.
  • Line n intersects both line r and line s.
  • At the intersection of line n and line r, 1 angle is labeled clockwise from top left as follows:
    • Top left: 162/li>
  • At the intersection of line n and line s, 1 angle is labeled clockwise from top left as follows:
    • Top left: x/li>
  • A note indies the figure is not drawn to scale.

In the figure, line n intersects lines r and s . Line r is parallel to line s . What is the value of x ?

Enter your answer:

Clockwise from top left, the 3 lines are labeled n, r, and s. Line n intersects

Medium-difficulty · SAT Math · Lines, Angles, and Triangles — Angle relationships (parallel lines). Read the question above, select your answer, and check the full explanation below to understand exactly why the correct choice works.

Answer explanation

The correct answer is 162 . It's given that line r is parallel to line s . Since line n intersects both lines r and s , it's a transversal. The angles in the figure marked as 162° and x° are on the same side of the transversal, where one is an interior angle with line s as a side, and the other is an exterior angle with line r as a side. Thus, the marked angles are corresponding angles. When two parallel lines are intersected by a transversal, corresponding angles are congruent and, therefore, have equal measure. It follows that the value of x is 162 .