Tip #4 to Get a Top SAT Math Score (page 2)

Every SAT has a bunch of geometry questions. Many students panic, "I don't remember the million stupid postulates we learned." Good news, you only need a small handful of those million postulates to solve most geometry questions.

Skills 4 through 7 show you how to find the measure of an angle in a diagram. Every SAT has several of these questions; memorize these skills and you will gain points, guaranteed.

1. Vertical angles are equal. a° = b°



2. The angles in a linear pair add up to 180°.



3. The angles in a triangle add up to 180°.

The angles in a 4-sided shape add up to 360°.

The angles in a 5-sided shape add up to 540°.

The angles in a 6-sided shape add up to 720°.

Let's look at this question;

Solution: This question uses two of our strategies: linear pair and 180° in a triangle. As soon as you see a linear pair of angles, determine the measures of the angles in the pair. So the angle next to the 140° must be 180° – 140° = 40°. Now we have two of three angles in a triangle which must add up to 180°, so the third must be 180° – 100° – 40° = 40°.

Correct answer: D

Example Problems

Easy

1. In the figure above, what is the value of m ?
   1. 150
   2. 80
   3. 73
   4. 27
   5. 53



2. In the figure above, what is the value of b ?
   1. 50
   2. 55
   3. 60
   4. 75
   5. 65
   6. 70



3. If y = 60 and points A, B, and C lie on the same line, what is the value of z ?
   1. 125
   2. 100
   3. 84
   4. 62
   5. 61

Medium



4. In the figure above, what is the value of z ?

Hard



5. In the figure above, if AB is a line, what is n in terms of m ?
   1. 180 – m
   2. 180 – 2m
   3. 
   4. 
   5. 

Answers

1. C   This question uses two of our eight strategies. As soon as you see a linear pair of angles, determine the measure of the unknown angle in the pair. So the angle next to 153° must be 180 – 153 = 27°. Now we have two of three angles in a triangle which must add up to 180, so the third must be 180 – 80 – 27 = 73.
2. B   This is essentially the same question as #1 above. But notice that this figure is not drawn to scale. Whenever this happens, just redraw it roughly to scale. This one is very easy. The angle next to 80° must be 180 – 80 = 100. Now we have two of three angles in a triangle which must add up to 180°, so the third must be 180 – 100 – 25 = 55.
3. C   Mark y = 60 into the figure, and as soon as you see a linear pair, solve the other angle, which in this case equals 180 – 60 = 120. Now we have 4 of the 5 angles of a five-sided figure. A five-sided figure has 540°, so 540 minus the other angles equals the measure of angle z. z = 540 – 120 – 133 – 139 – 64 = 84.
4. 30   Use the smaller triangle to determine x (2x + 75 + 45 + 180, so x = 30). Then use x to solve for the angles in the other triangle:

120 + 30 + z = 180

150 + z = 180

z = 30

5. E   The two angles form a linear pair, so 2m + 3n = 180. We need "n in terms of m," so we use algebra to solve for n:

2m + 3n = 180       subtract 2m

3n = 180 – 2m       divide by 3

Go to: Tip #5