Use the figure to answer the question.

Question

Use the figure to answer the question.

An inclined transversal passes through two vertical parallel lines labeled upper M and upper N. The angles formed around the intersection point of upper M are labeled clockwise, starting from the upper left quadrant: 1, 2, 4, and 3. The corresponding angles formed around the intersection point of upper N are labeled clockwise, starting from the upper left quadrant: 5, 6, 8, and 7.

If angle 4 is 42°
and lines M
and N
are parallel, give a reason why angle 5 is also 42°
.

Responses

Angle 4 and angle 5 are alternate interior angles, so their measures must be the same.
Angle 4 and angle 5 are alternate interior angles, so their measures must be the same. - not selected, this is the correct answer

Angle 4 and angle 5 are interior angles, so their measures must be the same.
Angle 4 and angle 5 are interior angles, so their measures must be the same. - incorrect

Angle 4 and angle 5 are vertical angles, so their measures are congruent.
Angle 4 and angle 5 are vertical angles, so their measures are congruent. - no response given

Angle 4 and angle 5 are corresponding angles, so their measures are congruent.

PLEASE SHOW THE WORK!

Answer 1

Angle 4 and angle 5 are alternate interior angles because they are on opposite sides of the transversal and inside the two parallel lines. According to the Alternate Interior Angles Theorem, when a transversal intersects two parallel lines, the alternate interior angles are congruent. Therefore, angle 4 and angle 5 must have the same measure.