Question

For line b, d, and e, line d is parallel to line e, and m∠1 = 81°.

Part A: In complete sentences, explain the relationships between all pairs of special angles 1, 2, 3, and 4 created by transversal line b and parallel lines d and e.

Part B: For the given diagram, use the measure of the special angle relationships created by transversal line b and parallel lines d and e to find the measures of ∠2, ∠3, and ∠4.

Answer 1

Part A:
For angles 4 and 3, they would be considered equal because they are alternative interior angles. And as for angles 1 and 2, these angles are supplementary to each other, meaning that the sim of both of these angles have a total of 180 degrees. In addition, angles 1 and 3 are vertical angles, meaning they are equal.

Part B:
If the measurement of angle 1 is equal to 81°, then due to the relationships stated in part A, the measurements of both angles 3 and 4 should equal 81° as well. And as for angle 2, I set up the equation 81+x=180. Giving me the degree measure of 2 being 99°.
Therefore-
<1=81°
<2=99°
<3=81°
<4=81°