Will give   given ∠10≅∠14, which lines, if any, must be parallel based on the given information? justify your conclusion a) c∥d, converse of the alternate exterior angles theorem b) a∥b, converse of the corresponding angles theorem c) a∥b, converse of the same-side interior angles theorem d) not enough information to make a conclusion

Looking at the diagram, â 10 and â 14 are corresponding angles with lines c and d, and line a is the transverse line that's intersecting lines c and d. Since â 10 and â 14 are congruent, that means that lines c & d are parallel to each other via the Converse of the Corresponding Angles Theorem. Unfortunately, none of the available 4 choices is correct. Choice A is wrong since it mentions the incorrect theorem Choices B & C are also wrong since they claim that lines a and b are parallel and you don't have enough information to justify that. Choice D is wrong because you do have enough information to make a conclusion. Now you can possibly claim that the correct answer is "A" because â 14 is congruent to â 16 due to them being vertical angles to each other. And since â 14 is congruent to â 10, that means that â 16 is also congruent to â 10. And â 16 and â 10 ARE Alternate Exterior Angles to each other. I'd recommend option "A" along with the explanation as to why â 16 and â 10 are congruent to each other.