Question

1. choose the conclusion that could be made using the given postulate and given lines a and b are parallel:

alternate exterior angles are congruent
a. ∠3 = ∠7
b. ∠7 = ∠6
c. ∠1 = ∠8
d. ∠4 is supplementary to ∠6

1. choose the conclusion that could be made using the given postulate and given lines a and b are parallel:

consecutive interior angles are supplementary
a. ∠3 + ∠7 = 180°
b. ∠7 + ∠6 = 180°
c. ∠1 + ∠8 = 180°
d. ∠4 + ∠6 = 180°

Explanation:

Question 7

Alternate exterior angles are non - adjacent exterior angles that lie on opposite sides of the transversal. For lines \(a\) and \(b\) (parallel) and a transversal, \(\angle3\) and \(\angle7\) are alternate exterior angles. By the alternate exterior angles congruence postulate, if two parallel lines are cut by a transversal, then alternate exterior angles are congruent.

Consecutive interior angles (also known as same - side interior angles) are two interior angles that lie on the same side of the transversal. For parallel lines \(a\) and \(b\) cut by a transversal, \(\angle4\) and \(\angle6\) are consecutive interior angles. By the consecutive interior angles supplementary postulate, if two parallel lines are cut by a transversal, then consecutive interior angles are supplementary.

Answer:

A. \(\angle3=\angle7\)

Question 8