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- Clockwise from top left, the 3 lines are labeled t, m, and n.
- Line t intersects both line m and line n.
- At the intersection of line t and line m, 1 angle is labeled clockwise from top left as follows:
- Bottom left: 170/li>
- At the intersection of line t and line n, 1 angle is labeled clockwise from top left as follows:
- Bottom left: w/li>
- A note indies the figure is not drawn to scale.
In the figure, line is parallel to line . What is the value of ?
Clockwise from top left, the 3 lines are labeled t, m, and n. Line t intersects
Easy-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
Choice D is correct. It's given that lines and are parallel. Since line intersects both lines and , it's a transversal. The angles in the figure marked as and are on the same side of the transversal, where one is an interior angle with line as a side, and the other is an exterior angle with line 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 . Therefore, the value of is .
Choice A is incorrect and may result from conceptual or calculation errors.
Choice B is incorrect and may result from conceptual or calculation errors.
Choice C is incorrect and may result from conceptual or calculation errors.
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