Question

which of the following are remote interior angles of ∠ 5? check all that apply. ∠1 ∠3 ∠5 ∠6 ∠2 ∠4

Explanation:

Step1: Recall remote interior angle definition

Remote interior angles of an exterior angle of a triangle are the two non - adjacent interior angles of the triangle. First, identify the exterior angle (∠5? Wait, the question is about ∠5? Wait, the original question: "Which of the following are remote interior angles of ∠5? Check all that apply." Wait, the diagram: there is a triangle with angles ∠1, ∠2, and the third angle at the intersection. The exterior angle ∠5, its adjacent angle would be ∠3 (vertical angles? Wait, no. Let's look at the triangle. The triangle has angles ∠1, ∠2, and the angle at the vertex where the two lines cross (let's call it ∠3). Then ∠5 is an exterior angle at that vertex. So the remote interior angles of ∠5 would be the two interior angles of the triangle that are not adjacent to ∠5. So ∠1 and ∠2 are the interior angles of the triangle. ∠5 is adjacent to ∠3 (linear pair or vertical? Wait, ∠3 and ∠5: if two lines intersect, ∠3 and ∠5 are adjacent (linear pair), ∠3 and ∠4 are vertical? Wait, no, the intersection of two lines creates vertical angles: ∠3 and ∠4, ∠5 and ∠6. Wait, the triangle has vertices: one with ∠1, one with ∠2, and one at the intersection of the two lines (angle ∠3). So ∠5 is an exterior angle at the ∠3 vertex. So the remote interior angles of ∠5 are the two interior angles of the triangle that are not adjacent to ∠5. So ∠1 and ∠2. Wait, but the options are ∠1, ∠2, ∠3, ∠4, ∠5, ∠6. Wait, maybe I misread. Wait, the question is about ∠5? Wait, the user's diagram: "Which of the following are remote interior angles of ∠5? Check all that apply." The triangle has ∠1, ∠2, and the angle at the intersection (∠3). ∠5 is adjacent to ∠3 (linear pair: ∠3 + ∠5 = 180°). So the remote interior angles of ∠5 (exterior angle) are the two interior angles of the triangle that are not adjacent to ∠5. So ∠1 and ∠2. Wait, but let's confirm the definition: Remote interior angles are the two non - adjacent interior angles to an exterior angle of a triangle. So for exterior angle ∠5, the adjacent interior angle is ∠3, so the remote ones are ∠1 and ∠2.

Step2: Check the options

The options are ∠1, ∠2, ∠3, ∠4, ∠5, ∠6. So ∠1 and ∠2 are the remote interior angles of ∠5. Wait, but maybe the question was about ∠4? Wait, the yellow highlight is ∠4. Wait, maybe a typo. Wait, the original question: "Which of the following are remote interior angles of ∠5? Check all that apply." Wait, the user's image: the question is "Which of the following are remote interior angles of ∠5? Check all that apply." The options are ∠1, ∠2, ∠3, ∠4, ∠5, ∠6. So according to the definition, remote interior angles of an exterior angle (∠5) are the two non - adjacent interior angles of the triangle. The triangle has interior angles ∠1, ∠2, and ∠3 (the angle at the intersection). ∠5 is adjacent to ∠3 (linear pair), so the non - adjacent (remote) interior angles are ∠1 and ∠2.

Answer:

∠1, ∠2 (So the correct options are the ones corresponding to ∠1 and ∠2. If the options are labeled as: ∠1 (option A), ∠2 (option B), ∠3 (option C), ∠4 (option D), ∠5 (option E), ∠6 (option F), then the answers are A. ∠1, B. ∠2)