Tip #7 to Get a Top SAT Math Score

By the end of this Skill, you will have learned all that you need to know about angles for the SAT. That's great news because every SAT includes several angle questions, and now you can always get them right. You know what to expect, you know what to use, and you will earn 30 or more points!

Here are the last two concepts for finding an angle:

1. An exterior angle equals the sum of the two far away interior angles.



2. "Bisect" means to cut into two equal parts. An angle bisector cuts an angle into two equal parts, and a segment bisector cuts a segment into two equal parts.

Let's look at this question:

Solution: This is essentially a question from Skill 4, but this time we know the exterior angle trick. Since an exterior angle equals the sum of the two far away interior angles, 80 = 25 + b. So b = 55.

Correct answer: B

Example Problems

Medium

1. In the figure above, what is the value of y – x ?



2. In the figure above, segments AC and BD intersect at E. If the measure of AEB is 70° and segment EF (not shown) bisects BEC, what is the measure of FED ?

Hard



3. In the figure above, if x = 71, what is the value of y + z ?
   1. 71
   2. 142
   3. 211
   4. 251
   5. 282



4. In the figure above, the dotted lines bisect angles with measures x° and y°. In terms of x and y, what is the value of z ?
   1. 180 – 0.5(x + y)
   2. 0.5(x + y)
   3. 180 – (x + y)
   4. 180 + (x – y)
   5. 90 – 0.5(x – y)

Answers

1. 90   We've seen this question before, but now we have even more Skills to answer it. Look for our strategies. Are there vertical angles we can use? No. Linear pairs? Maybe. Triangles? Shaboom! 2x + 75 + 45 = 180, use algebra to get x = 30 and plug that into the other triangle. So 30 + 30 + y = 180. Use algebra to get y = 120. Also Skill 7 gives us a shortcut here since y is an exterior angle to the first triangle and must equal 45 + 75. So, y – x = 120 – 30 = 90.
2. 125   First, label all info that is given in the question into the diagram. Since the measure of is 70, must also be 70 since they are vertical angles. Then makes a linear pair with and must be 180 – 70 = 110. If segment EF (not shown) bisects , then is 55, half of 110. So equals 55 + 70 = 125.
3. D   The vertical angle of x in the triangle is 71, so the other two angles of the triangle add up to 180 – 71 = 109. Each of these angles makes a linear pair with y and z, respectively. So these two angles plus y and z make two linear pairs and equal 2(180). Therefore, 109 + y + z = 360. So use algebra to get y + z alone. In math class this would be unusual. You teacher usually wants you to solve for just y or just z, but sometimes the SAT asks for y + z, so we solve for that. No problem. y + z = 360 – 109 = 251.
4. A   The dotted lines form a small triangle inside the larger triangle. Since the dotted lines bisect angles x and y, the angles of this triangle are z, . "What is the value of z?" means solve for z. So z = . This does not initially seem to match any answers, but .

Go to: Tip #8