Generally:
- Vertical angles are congruent. An example of vertical angles on the diagram are angles 1 and 4; they are opposite each other on the two intersecting lines.
When two parallel lines are intersected by a transversal:
- Corresponding angles are congruent. Corresponding angles are angles on the same side of the transversal with corresponding positions, such as angles 2 and 5 in the diagram.
- Alternate interior angles are congruent. Angles 3 and 5 are an example of alternate interior angles on the diagram. They are contained within the interior of the two parallel lines, and are on opposite sides of the transversal.
- Alternate exterior angles are congruent. These angles lie on the outside of the parallel lines and on opposite sides of the transversal. Angles 1 and 7 are an example of alternate exterior angles.
Looking at the diagram, we can recognize that our given angle of 56° creates a vertical angle pair with angle 7; these angles are congruent. Additionally, since corresponding angles are congruent, angles 4 and 7 are congruent. Notice that angle 4 creates a vertical angle pair with angle 1, and that angle 1 also corresponds to the given angle.
Answer:
The angles which are congruent to the given angle measure are:
∠1, ∠4 and ∠7