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

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
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
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

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
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

Answers

C Easy! In a pair of parallel lines there are only two kinds of angles, big and little, and the two add up to 180. Since y = 45, x = 180 – 45 = 135.
D Parallel lines cut by a transversal make 2 kinds of angles, big and little. Clearly x is little and z is big. If x = 66, then z = 180 – 66 = 114.
A First, mark the info that is given in the question into the diagram. That always helps to make the question simpler and usually shows which of our geometry strategies to use. Then use vertical angles, linear pairs, triangles, etc. to calculate the measures of any other angles that you can. The vertical angle to z is 40, and the linear pair to x is 50, so now we have two angles of the triangle. 180 – 50 – 40 = 90, so the linear pair of y is 90 and is therefore y = 180 – 90 = 90.
B Mark the info from the question into the diagram. Then mark all other angles that you can determine. Now x and y are a linear pair, so x + y = 180 and x = 180 – 95 = 85. Since the figure is not drawn to scale, you can resketch it to scale. When you do this, you notice that if z and x are both less than 90, the lines cannot be parallel—they are heading toward each other and will intersect. Only choice B is true.
E Use the strategies. Mark x = 22. Therefore, in the triangle, the missing angle is 180 – 108 – 22 = 50. And in the pair of parallel lines y is a big, not a little, angle; thus it equals 180 – 50 = 130.

Go to: Tip #6

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