Question

Two parallel lines are cut by a transversal and angles 1 and 7 are alternate exterior angles. If angle 1 measures 120 degrees , how does angle 7 compare with angle 1?

A.Angle 7 is supplementary with angle 1
B.Angle 7 and angle 1 are congruent.
C.The angles cannot be compared.

Answer 1

Answer: The correct option is B; Angle 7 and angle 1 are congruent

Step-by-step explanation: Please refer to the picture attached for more details. The parallel lines AB and CD have been drawn and a transversal line have also been drawn to cut both lines as shown in the picture.

Since both lines are parallel, the angles formed by the transversal would be equal.

A careful observation would show that the interior angle formed by the transversal (which is the supplement of angle 120), is equal or congruent to the interior angle formed at angle 7. These are commonly referred to as "z angles" by virtue of the shape formed. Angle 1 and angle 7 are the exterior alternate angles formed by the transversal and they are both congruent, that is, they both have the same measurement.

The angles cannot be described as supplementary, because supplementary angles add up to 180 degrees. That is, if angle A plus angle B equals 180, then angles A and B are both supplementary. This does not apply to angle 1 and angle 7.

Answer 2

Answer: B.Angle 7 and angle 1 are congruent.

Explanation:

Alternate angles means that the angles are formed on the alternating sides of the transversal. The term "exterior" means that the alternate angles are formed outside the parallel lines.

Since the parallel lines are cut by a transversal and angles 1 and 7 are alternate exterior angles, it means that angles 1 and 7 are equal or congruent. This is because of the rule in geometry stating that two alternate exterior angles are congruent. Therefore, the correct option would be

B. Angle 7 and angle 1 are congruent.