The GRE makes frequent use of diagrams that include parallel lines cut by a transversal.
Notice that there are eight angles formed by this construction, but there are only two different angle measures (a and b). All the acute angles (less than 90°) in this diagram are equal. Likewise, all the obtuse angles (more than 90° but less than 180°) are equal. The acute angles are supplementary to the obtuse angles. Thus, a + b = 180°.
When you see a third line intersecting two lines that you know to be parallel, fill in all the a (acute) and b (obtuse) angles, just as in the diagram here.
Sometimes the GRE disguises the parallel lines and the transversal so that they are not readily apparent, as in the diagram pictured to the right.
In these disguised cases, it is a good idea to extend the lines so that you can easily see the parallel lines and the transversal. Just remember always to be on the lookout for parallel lines. When you see them, extend lines and label the acute and obtuse angles.
You might also mark the parallel lines with arrows.
Refer to the following diagram for questions #4–5.
If g = 120, what is a?
If g = 120, what is a + b + c?