A
B
C
D
Explanation
Correct answer: D.
Choice D is correct. It's given that triangle is similar to triangle , such that , , and correspond to , , and , respectively. Therefore, side corresponds to side . Since the length of each side of triangle is times the length of its corresponding side in triangle , it follows that the measure of side is times the measure of side . Thus, since the measure of side is , then the measure of side is , or .
Desmos solution:
Enter in Desmos:
Reviewed and rewritten by CookSAT
Why the other choices are wrong
Choice A
Choice A is incorrect and may result from conceptual or calculation errors.
Choice B
Choice B is incorrect. This is the measure of side , not side .
Choice C
Choice C is incorrect and may result from conceptual or calculation errors.