SAT Lines, angles, and triangles Question

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Question 1 · Medium · MathMay 2025 Batch 3 · Q2Lines, angles, and triangles · 0 solved

Question graph or diagram from the source SAT PDF.

Note: Figure not drawn to scale. In the figure shown, line $l$ intersects lines $j$ and $k$ . Which additional piece of information is sufficient to prove that lines $j$ and $k$ are parallel?

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Strategy

Look for a parallel-line theorem that matches the angle relationship shown: corresponding angles, alternate interior angles, or same-side interior angles. Then use the given measure to see whether it creates one of those relationships between the two lines cut by the transversal.

Hints (open one at a time)

Hint 1

Focus on how the upper angle and the 54° angle are positioned relative to the transversal and the two lines.

Hint 2

Try a parallel-line test: if two angles have the same relative location at the two intersections, equal measures can prove the lines are parallel.

Hint 3

See which extra fact makes one angle match the 54° angle in the correct matching position; that is the one that can justify j and k being parallel.

Step-by-step Explanation

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