OG详解-OG4 数学2 Q16

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 m intersect. It follows that the angle with measure xº and the angle with measure yº are vertical angles, so x = y. It’s given that x = 6k +13 and y = 8k -29. Substituting 6k +13 for x and 8k -29 for y in the equation x =  yields 6k +13 = 8k -29. Subtracting 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 angles with measures yº and zº 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.