OG详解-OG8 数学2 Q24

Choice C is correct. Since P =(4,5) and Q =(4,7), side PQ is parallel to the y-axis and has a length of 2. Since P =(4,5) and R =(6,5), side PR is parallel to the x-axis and has a length of 2. Therefore, triangle PQR is a right isosceles triangle, where ∠P has measure 90° and ∠Q and ∠R each have measure 45°. It follows that if the measure of ∠Q is t°, then t = 45. Since L =(4,5) and M =(4,7+k) , side LM is parallel to the y-axis and has a length of k + 2. Since L = (4,5)and N =(6+k,5）, 5h, side LN is parallel to the x-axis and has a length of k + 2. Therefore, triangle LMN is a right isosceles triangle, where ∠L has measure 90° and ∠M and ∠N each have measure 45°. Of the given choices, only (90-t)° is equal to 45°, so the measure of ∠N is (90-t)°.
Choice A is incorrect and may result from conceptual or calculation errors. Choice B is incorrect and may result from conceptual or calculation errors. Choice D is incorrect and may result from conceptual or calculation errors.