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° .
Angle 4 and angle 5 are alternate 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.
The correct reason is: 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 correct reason is: Angle 4 and angle 5 are alternate interior angles, so their measures must be the same.
To understand why angle 5 must also be 42°, you can use the concept of parallel lines and transversals. When two parallel lines are intersected by a transversal, certain pairs of angles are formed.
In this case, lines M and N are parallel, and the inclined transversal passes through them. Angle 4 is formed by the intersection of line M and the transversal. Angle 5, on the other hand, is formed by the intersection of line N and the same transversal.
Alternate interior angles are a pair of angles that are on the opposite sides of the transversal, between the two parallel lines. These angles are congruent, meaning they have the same measure.
Since angle 4 and angle 5 are alternate interior angles, and angle 4 is given to be 42°, it follows that angle 5 must also be 42°. Therefore, the reason why angle 5 is also 42° is that angle 4 and angle 5 are alternate interior angles.