Me !
for line b, d, and e, line d is parallel to line e and ∠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 following special angle relationships are created by transversal line b and parallel lines d and e : 1 to find the measures of ∠2, ∠3, and ∠4.

Part a
because line b is intersecting the two parallel lines (d and e), eight angles are formed. line b is called a transversal since it passes through at least two lines. these angles form 4 pairs of corresponding angles. corresponding angles are those that angles are in matching corners (like  ∠ 1 and  ∠ 4 in your diagram). corresponding angles are congruent, which means they have the same angle measurement. angles that are inside of the parallel lines (like  ∠ 3 and ∠4) are called interior angles. angles outside of the parallel lines (like  ∠ 1 and ∠ 2) are called exterior angles. alternate angles (such as ∠2 and ∠4) are on opposite sides of the transversal (line b).

part b
1. from the information above, you were given the measurement of  ∠ 1, which is 81°. 
2. together  ∠1 and  ∠2 equal 180°. take 180° and subtract the measurement of  ∠1 to find the measurement of  ∠2. 180 - 81 = 99, so the measurement of  ∠2 = 99°.
3.  ∠3 is congruent to  ∠1, so its measurement is also 81°.
4.  ∠4 and  ∠2 are corresponding angles, so the measurement of  ∠4 is also 99°