Question

Short Response 16. Parallel lines p and q are cut by transversal t to form angles 1-8. If 22 and 27 are alter- nate exterior angles, 27 and 26 are vertical angles, and 26 and 24 are consecutive interior angles, what can you conclude about the relationship between the angle measures of 22 and 24? Explain.

I don’t understand how to solve this, please help!!​

Answer 1

see below (I hope this helps!)

Explanation:

Alternate exterior angles are congruent so we know that ∠2 ≅ ∠ 7. Vertical angles are also congruent so ∠7 ≅ ∠6. Consecutive interior angles are supplementary so we know that ∠6 and ∠4 are supplementary. Now, we can use the Transitive Property (this states that if a = b and b = c then a = c) to compare ∠2 and ∠4. In this case, a = ∠2, b = ∠7 and c = ∠6 so we know that ∠2 ≅ ∠6 and since ∠6 is supplementary to ∠4, we can use the Transitive Property again to conclude that ∠2 and ∠4 are supplementary.