Question

given that $overline{ba}paralleloverline{ce}$, select which type of angle each pair below is and then tell whether the pair is congruent or supplementary.
(a) 7. $angle bae$ and $angle ced$
a. interior angles on the same side of the transversal; congruent
b. corresponding angles; congruent
c. alternate exterior angles; congruent
d. adjacent angles; congruent
e. alternate interior angles; congruent

1. $angle abc$ and $angle bce$

a. interior angles on the same side of the transversal; supplementary
b. adjacent angles; supplementary
c. alternate exterior angles; congruent
d. corresponding angles; congruent
e. alternate interior angles; congruent

1. $angle bce$ and $angle ecd$

a. adjacent angles (linear pair); supplementary
b. corresponding angles; supplementary
c. alternate exterior angles; congruent
d. interior angles on the same side of the transversal; supplementary
e. alternate interior angles; supplementary

Explanation:

Step1: Recall angle - pair relationships

When two parallel lines are cut by a transversal, different types of angle - pairs are formed with specific congruence or supplementary relationships.

Step2: Analyze ∠BAE and ∠CED

Since \(\overline{BA}\parallel\overline{CE}\), ∠BAE and ∠CED are alternate interior angles. Alternate interior angles are congruent when the lines are parallel.

Step3: Analyze ∠ABC and ∠BCE

∠ABC and ∠BCE are alternate interior angles. Alternate interior angles are congruent when the lines are parallel.

Step4: Analyze ∠BCE and ∠ECD

∠BCE and ∠ECD form a linear - pair. A linear - pair of angles is adjacent and supplementary.

Answer:

1. E. Alternate interior angles; congruent
2. E. Alternate interior angles; congruent
3. A. Adjacent angles (linear pair); supplementary