Tip #5 to Get a Top SAT Math Score

In math class, learning about parallel lines can seem pretty tricky—alternate interior angles, corresponding angles, same-side interior angles. … We don't need all that for the SAT. We just need to know that

• Parallel lines are two lines that never touch.
• If two parallel lines are crossed by another line (called a transversal), then eight angles form.
• These eight angles are of two types, big or little. All bigs are equal, and all littles are equal.

This is enough to answer any parallel-lines SAT question. There's another 10 points!

Let's look at this question:

Solution: First, always mark any info from the question into the diagram, so mark x = 45. Remember SAT Math Mantra #4: when you are given two angles of a triangle, always determine the third: 180° – 108° – 45° = 27°. Next, in the pair of parallel lines, there are only two kinds of angles, big and little. Angle y is big, not little, so it equals 180° – 27° = 153°.

Example Problems

Easy

1. In the figure below, m || n. If y = 45, what is the value of x ?
   
   1. 45
   2. 100
   3. 135
   4. 145
   5. 180
2. If x = 66 and p || q and m || n in the four lines shown, what is the value of z ?
   
   1. 24
   2. 66
   3. 90
   4. 114
   5. 166
3. In the figure below, m || n. If z = 40 and x = 130, then y =
   
   1. 90
   2. 80
   3. 40
   4. 50
   5. 20

Medium

4. If z = 45 and y = 95 in the figure below, then which of the following must be true?
   
   1. p || q
   2. x + y = 180
   3. z = x
   4. x + z = 180
   5. y = 2x
5. In the figure below, if a || b and the measure of x = 22, what is the measure of y?
   
   1. 22
   2. 50
   3. 90
   4. 108
   5. 130