SAT Math Multiple Choice Practice Question 583: Answer and Explanation

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Question: 583

19.

Based on the figure above, which of the following expressions is equal to b ?

A. ac
B. 180 – (a + c)
C. (a + c) – 90
D. (a + c) – 180
E. 360 – (a + c)

Correct Answer: D

Explanation:

D Plug in on geometry if there are variables in the equation. In the figure, the angle marked a° looks bigger than 90° so make a = 150. The value of c should be something different, such as c = 140. Now we have information to figure out two of the angles of the triangle in which we find b. There are 180° in a straight line, so the angle on the left is 180 – 150 = 30 and the angle on the right is 180 – 140 = 40. There are 180° in a triangle, so 180 = b + 30 + 40, and b = 110, which is our target number. After replacing a and c in the answers with 150 and 140, respectively, only D equals 110. A gives 10; B gives –110; C gives 200; E gives 70.

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