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

Question

In the figure shown, lines $r$ and $s$ are parallel, and line $m$ intersects both lines. If $y less than 65$ , which of the following must be true?

Accepted Answer

Choice B is correct. In the figure shown, the angle measuring y &#176; is congruent to its vertical angle formed by lines s and m , so the measure of the vertical angle is also y &#176; . The vertical angle forms a same-side interior angle pair with the angle measuring x &#176; . It's given that lines r and s 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 x &#176; is 180 &#176; , or x + y = 180 . Subtracting x from both sides of this equation yields y = 180 - x . Substituting 180 - x for y in the inequality y &#60; 65 yields 180 - x &#60; 65 . Adding x to both sides of this inequality yields 180 &#60; 65 + x . Subtracting 65 from both sides of this inequality yields 115 &#60; x , or x &#62; 115 . Thus, if y &#60; 65 , it must be true that x &#62; 115 . Choice A is incorrect and may result from conceptual or calculation errors. Choice C is incorrect. x + y must be equal to, not less than, 180 . Choice D is incorrect. x + y must be equal to, not greater than, 180 .

Question 57d14e