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Choice C is correct. Vertical angles, which are angles that are opposite each other when two lines intersect, are congruent. The figure shows that lines t and o m intersect. It follows that the angle with measure x and the angle with o = = + measure y are vertical angles, so x y. It’s given that 6x 1k3 and = - + - = 8y 2k9. Substituting 6k 13 for x and 8k 29 for y in the equation x y + = - yields 6 13 8k 29. Sukbtracting 6k from both sides of this equation yields = - = = 13 2k 29. Adding 29 to both sides of this equation yields 42 2k, or 2k 42. = Dividing both sides of this equation by 2 yields k 21. It’s given that lines m and n are parallel, and the figure shows that lines m and n are intersected by a transversal, line t. If two parallel lines are intersected by a transversal, then the same-side interior angles are supplementary. It follows that the same-side interior 48 SAT PRACTICE TEST #4 ANSWER EXPLANATIONS SAT ANSWER EXPLANATIONS nnn MATH: MODULE 2 o o + = angles with measures y and z are supplementary, so y z 180. Substituting - - + = 8k 29 for y in this equation yields 8k 29 z 180. Substituting 21 for k in ( )- + = + = this equation yields 8 21 29 z 180, or 139 z 180. Subtracting 139 from = both sides of this equation yields z 41. Therefore, the value of z is 41. Choice A is incorrect and may result from conceptual or calculation errors. Choice B is incorrect. This is the value of k, not z. Choice D is incorrect. This is the value of x or y, not z.