If angle 4 is 42° and lines M and N are parallel, give a reason why angle 5 is also 42°.
(Parallel lines)
1. Angle 4 and angle 5 are interior angels, so their measures must be the same
2. Angle 4 and angle 5 are corresponding angles, so their measure's are congruent
3. Angle 4 and angle 5 are alternate interior angles, so their measures must be the same
4 Angle 4 and angle 5 are vertical angles, so their measures are congruent
The correct reason is option 4. Angle 4 and angle 5 are vertical angles, which means they are opposite each other and congruent. Therefore, if angle 4 is 42°, angle 5 must also be 42°.
The correct reason why angle 5 is also 42° is because angle 4 and angle 5 are corresponding angles.
When two parallel lines are intersected by a transversal, corresponding angles are formed. Corresponding angles are formed on the same side of the transversal and in corresponding positions. They are always congruent or equal in measure.
Therefore, since angle 4 is 42°, angle 5, being its corresponding angle, will also be 42°.