Complementary angles are angles whose sum is 90°
Supplementary angles are angles whose sum is 180°
Vertical angles are the angles opposite of each other at the intersection of two lines. They are called vertical angles because they share a common vertex. Vertical angles always have equal measures.
Alternate interior angles are formed when there exists a transversal. They are the angles on opposite sides of the transversal, but inside the two lines the transversal intersects. Alternate interior angles are congruent to each other if (and only if) the two lines intersected by the transversal are parallel. An easy way of identifying alternate interior angles is by drawing the letter "Z" (forwards and backwards) on the lines as shown below.Similar to alternate interior angles, alternate exterior angles are also congruent to each other if (and only if) the two lines intersected by the transversal are parallel. These angles are on opposite sides of the transversal, but outside the two lines the transversal intersects.Corresponding angles are the pairs of angles on the same side of the transversal and on corresponding sides of the two other lines. These angles are equal in degree measure when the two lines intersected by the transversal are parallel.