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° .
(1 point)
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.
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.
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.
Angle 4 and angle 5 are corresponding angles, so their measures are congruent.
Angle 4 and angle 5 are vertical angles, so their measures are congruent.
Angle 4 and angle 5 are corresponding angles, so their measures are congruent.
The correct answer is "Angle 4 and angle 5 are corresponding angles, so their measures are congruent."
To understand why angle 4 and angle 5 are congruent, let's review corresponding angles. Corresponding angles are formed when a transversal intersects two parallel lines. When this happens, each angle on one side of the transversal has a corresponding angle on the other side of the transversal.
In this case, angle 4 and angle 5 are both formed by the transversal intersecting lines M and N. They are corresponding angles because they are in the same relative positions on their respective parallel lines. Since angle 4 measures 42°, we can conclude that angle 5 also measures 42° because corresponding angles have equal measures.