Question

marisol claims that each pair of remote interior angles in a triangle has two exterior angles. do you agree? use a diagram to support your answer. choose the correct answer below. ○ a. diagram: triangle with angles 1,2; line extending, angle 3 no, ∠3 is the only exterior angle for remote interior angles ∠1 and ∠2. ○ b. diagram: triangle with angles 1,2,3 no, ∠3 is the only exterior angle for remote interior angles ∠1 and ∠2. ○ c. diagram: triangle with angles 1,2; exterior angles 3,4 yes, ∠1 and ∠2 are both remote interior angles for ∠3 and ∠4. ○ d. diagram: triangle with angles 1,2; exterior angles 3,4 yes, ∠1 and ∠2 are both remote interior angles for ∠3 and ∠4.

Explanation:

To determine the correct answer, we analyze the concept of remote interior angles and exterior angles in a triangle. A remote interior angle is an interior angle that is not adjacent to a given exterior angle. For a pair of remote interior angles (e.g., ∠1 and ∠2), there should be two exterior angles (vertical angles) formed at the vertex opposite to the side extended.

• Option A: Incorrect, as there should be two exterior angles (vertical angles) for ∠1 and ∠2.
• Option B: Incorrect, same reason as A.
• Option C: Incorrect, the labeling of ∠4 is not adjacent to ∠2 properly.
• Option D: Correct, ∠3 and ∠4 are vertical angles (exterior angles) and ∠1 and ∠2 are remote interior angles for both, showing two exterior angles for the pair.

Answer:

D. Yes, ∠1 and ∠2 are both remote interior angles for ∠3 and ∠4