SAT Lines, angles, and triangles Question

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Question 1 · Medium · MathMarch 2025 Batch 3 · Q12Lines, 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 $k$ intersects lines $r$ and $s$ . If $w = 146$ , which additional piece of information is sufficient to prove that lines $r$ and $s$ are parallel?

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Strategy

When a transversal crosses two lines, look for a converse angle relationship that proves parallel lines: corresponding angles congruent, alternate interior angles congruent, or same-side interior angles supplementary. Use the given angle measure to see whether the new information creates one of those proof patterns.

Hints (open one at a time)

Hint 1

Focus on the angle at the second intersection that lines up with the given angle at the first intersection.

Hint 2

A proof of parallel lines usually comes from matching angles being equal or a same-side pair adding to 180°.

Hint 3

If the second intersection gives an angle equal to 146°, you can match it with w as a corresponding angle and conclude the lines are parallel.

Step-by-step Explanation

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