Solve a geometry problem asking you to determine all eight angles created by two parallel lines and a transversal. Typically, you will be given the measure of one angle and then asked to determine the other seven. You will also need to know the terminology of the various pairs of angles.
Examine A and D in the top cluster of angles in a typical problem. They are called vertical or opposite angles, and by definition vertical angles are equal. Also recognize that angles such as A and B or A and C are called adjacent angles. In the case of parallel lines and transversals, all adjacent angles add up to 180 degrees. So if angle B is 37 degrees, you would subtract 37 from 180 to calculate that angle A equals 143 degrees. And angle C would also equal 37 degrees because angles B and C are vertical angles.
Recognize that angles on the top tier that correspond to angles on the bottom tier -- such as angles A and E or angles B and F-- are called corresponding angles and are always congruent when a transversal intersects two parallel lines. Only when the transversal is perpendicular to the two parallel lines and thus forms angles of 90 degrees are all eight of the angles equal.
Look at angles C and F and angles D and E. These pairs are called alternate interior angles. They are on opposite sides of the transversal, and inside the two parallel lines. By definition, each pair of alternate interior angles is congruent.
Examine angles B and G and angles A and H. Each of these pairs, called alternate exterior angles, are equal. They are on opposite sides of the transversal, and on the outside of the two parallel lines.
Look at angles A and G. They are supplementary but also nonadjacent, meaning they add up to 180 degrees. Angles D and F are also not adjacent but supplementary.
Memorize the definitions of vertical, adjacent, corresponding, alternate interior and alternate exterior angles to calculate all the angle measurements defined by a transversal, provided you're given the measurement of one angle.