What happens when a line intersects a bunch of parallel lines?

You can expect questions in the GRE about a line that intersects a pair of parallel lines and in the process creates angle pairs. Let’s take a detailed look at them and understand the properties of these angle pairs. In the following figure, line   intersects a pair of parallel lines  and . Total of 8 angles are formed as a result of the intersection. The following figure shows these 8 angles.

  

The important thing to remember is that all angles shown in blue are equal to each other and all angles shown in red are equal to each other.

In addition you also get pairs of supplementary angles e.g. in the above figure a red angle and a  blue angle are supplementary to each other. In other words blue + red = 180º

Example:

In the above figure, if line   intersects parallel lines   and  , what is the value of ?

A) 

B) 

C) 

D) 

E) 

Solution:

Step 1: Angles and are corresponding angles and therefore . Plugging in the  in the expression, we get:

Step 2: Angles and are supplementary angles and therefore . Substituting  in the expression we get:

Since  can not be negative, we can immediately rule out the first three options.

Step 3: However angles   and   are supplementary angles and therefore .

The correct answer is D