- Clockwise from top left, the 3 lines are labeled m, r, and s.
- Line m intersects both line r and line s.
- At the intersection of line m and line r, 1 angle is labeled clockwise from top left as follows:
- Top right: x°
- At the intersection of line m and line s, 1 angle is labeled clockwise from top left as follows:
- Bottom right: y°
- A note indicates the figure is not drawn to scale.
In the figure shown, lines and are parallel, and line intersects both lines. If , which of the following must be true?
Correct answer: B
Explanation
Choice B is correct. In the figure shown, the angle measuring is congruent to its vertical angle formed by lines and , so the measure of the vertical angle is also . The vertical angle forms a same-side interior angle pair with the angle measuring . It's given that lines and are parallel. Therefore, same-side interior angles in the figure are supplementary, which means the sum of the measure of the vertical angle and the measure of the angle measuring is , or . Subtracting from both sides of this equation yields . Substituting for in the inequality yields . Adding to both sides of this inequality yields . Subtracting from both sides of this inequality yields , or . Thus, if , it must be true that .
Choice A is incorrect and may result from conceptual or calculation errors.
Choice C is incorrect. must be equal to, not less than, .
Choice D is incorrect. must be equal to, not greater than, .
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