How do you classify a pair of angles?

Classifying pairs of angles ...

Vertical Angles

Vertical angles are formed by two intersecting lines. They are a pair of angles that are across from one another and always have the same degree measurement.

Adjacent Angles

Adjacent angles are a pair of angles that share a side and a vertex but do not overlap.

Complementary angles

Complementary angles are a pair of angles that add up to 90o. Placing complementary angles together forms a right angle.

Supplementary angles

Supplementary angles are a pair of angles that add up to 180o. Placing supplementary angles together forms a straight line.

Corresponding angles

Corresponding angles are formed when a pair of parallel lines is intersected by a third line (also called a transversal line). They are a pair of angles that are at corresponding positions but are not adjacent angles. Corresponding angles are on the same side of the transversal line and always have the same degree measurement.

Alternate Interior Angles

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.

Alternate Exterior Angles

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.