name all interior angles that are congruent to <15. State two theroems about congruence in parallel lines cut by a transversal that justify your answers?

A diagram is needed for this problem.

To find all the interior angles that are congruent to angle 15, we need to consider the properties of parallel lines cut by a transversal.

In this case, the transversal line intersects two parallel lines, creating corresponding angles, alternate interior angles, alternate exterior angles, consecutive interior angles, and vertical angles. Remember that these angles will be congruent if the lines are parallel.

First, let's find the angles that are congruent to angle 15.

Corresponding angles: The corresponding angle to angle 15 is the angle that is in the same position on the other parallel line. By the Corresponding Angles Theorem, we know that corresponding angles are congruent, so the corresponding angle to angle 15 will also be congruent.

Alternate interior angles: The alternate interior angles lie on the opposite sides of the transversal, between the parallel lines. By the Alternate Interior Angles Theorem, we know that alternate interior angles are congruent. Therefore, any alternate interior angle that corresponds to angle 15 will also be congruent to it.

Now, let's discuss the theorems that justify these answers:

1. Corresponding Angles Theorem: When a transversal intersects two parallel lines, the corresponding angles formed are congruent. This theorem is used to justify that the corresponding angle to angle 15 is congruent to it.

2. Alternate Interior Angles Theorem: When a transversal intersects two parallel lines, the alternate interior angles formed are congruent. This theorem is used to justify that any alternate interior angle corresponding to angle 15 is congruent to it.

By identifying the corresponding angle and considering the alternate interior angles, we can conclude that any angle corresponding to angle 15 and any alternate interior angle corresponding to angle 15 will be congruent to it.