If angle 4 is 42 deg and lines M and N are parallel, give a reason why angle 5 is also 42
If lines M and N are parallel, then angle 4 and angle 5 are corresponding angles. Corresponding angles formed by a transversal and two parallel lines are congruent. Therefore, if angle 4 measures 42 degrees, then angle 5 must also measure 42 degrees.
To determine why angle 5 is also 42 degrees, we need to understand the properties of parallel lines and their corresponding angles.
When two lines, such as M and N, are parallel, any transversal line that intersects them creates pairs of corresponding angles. Corresponding angles are formed when a transversal intersects two parallel lines, and they are located in the same relative positions at each intersection point.
In this case, angle 4 and angle 5 are corresponding angles, meaning they are located in the same relative positions where lines M and N intersect. Corresponding angles are always equal when the lines being intersected are parallel.
Given that angle 4 measures 42 degrees, we can conclude that angle 5 also measures 42 degrees because they are corresponding angles formed by the intersection of parallel lines M and N.