If M and N are parallel and angle 7 is 58°%0D%0A58%0D%0A°%0D%0A , what other angles are also 58°%0D%0A58%0D%0A°%0D%0A ? How do you know?
If M and N are parallel lines and angle 7 is 58°, then all corresponding angles that are formed by a transversal intersecting M and N will also measure 58°. These corresponding angles are typically denoted by listing them in sequence with the corresponding vertex from each line.
For example, if angle 7 is 58°, then the other corresponding angles that are also 58° can be denoted as angle 3, angle 6, and angle 2. These angles are formed by the transversal intersecting lines M and N.
We know this because when a transversal intersects parallel lines, it creates a series of alternate interior angles, same-side interior angles, and corresponding angles that are congruent to each other. In this case, angle 7 and angle 3 are corresponding angles and will have the same measure of 58°. Similarly, angle 7 and angle 6 as well as angle 7 and angle 2 will also have measures of 58° since they are corresponding angles formed by the transversal.