SAT Math Multiple Choice Practice Question 512: Answer and Explanation

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Question: 512


If PQRS is a parallelogram, then which of the following must be equal to x?

A. 180 – b
B. 180 – c
C. a + b
D. a + c
E. b + c

Correct Answer: E


E There are variables in the answer choices, so plug in. However, you can't plug in a value for all the variables at once because you must follow the rules of geometry. (Makes sense, right? It's the last question in the section.) Let's start by saying a = 70 and b = 60. Because PQRS is a parallelogram, angle Q must equal angle S, so angle S also equals 60. If you look at the big triangle that contains a and c, you already know that two of the angles are 60 and 70, so the third angle, c, must be 50. You know that PQ and SR are parallel and, you can see that x is a big angle and a is a small angle. So a + x = 180. Because a = 70, that means x = 110. Therefore, your target answer is 110. Plug your values for a, b, and c into the answers and you'll find that E equals 110.

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