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 corresponding angles, so their measures are congruent.
Angle 4 and angle 5 are corresponding angles, so their measures are congruent.
Angle 4 and angle 5 are corresponding angles, so their measures are congruent.
The reason why angle 5 is also 42° is that angle 4 and angle 5 are alternate interior angles. When a transversal intersects two parallel lines, the alternate interior angles are congruent, meaning their measures are the same. Therefore, since angle 4 is given to be 42°, angle 5 must also be 42°.
Use the figure to answer the question.
Two intersecting lines form an x and have four angles at the point of intersection labeled clockwise from the top: 1, 2, 3, and 4.
If angle 1 in the picture is 63° , what is the measure of angle 3? Why?
(1 point)
Responses
Angle 3 is 63° because angle 1 and angle 3 are corresponding angles.
Angle 3 is 63 degrees because angle 1 and angle 3 are corresponding angles.
Angle 3 is 63° because angle 1 and angle 3 are vertical angles.
Angle 3 is 63 degrees because angle 1 and angle 3 are vertical angles.
Angle 3 is 117° because angle 1 and angle 3 form a line.
Angle 3 is 117 degrees because angle 1 and angle 3 form a line.
There is not enough information in the figure to establish this.