PSAT Math Multiple-Choice Question 84: Answer and Explanation

Question: 84

In the figure above, what is the value of b, in terms of a?

• A. 30 - a
• B. 30 + a
• C. 60 + a
• D. 80 - a

Correct Answer: B

Explanation:

B

The question asks for the value of an angle in the figure. There are variables in the answer choices, so plug in. Make a = 90. The third angle will be 60°. Since the 60° angle and b° are supplementary angles, 60 + b = 180. Subtract 60 from both sides to get b = 180 - 60 = 120. This is the target value; circle it. Now plug a = 90 into the answer choices to see which one matches the target value. Choice (A) becomes 30 - 90 = -60. This does not match the target, so eliminate (A). Choice (B) becomes 30 + 90 = 120. Keep (B), but check (C) and (D) just in case. Choice (C) becomes 60 + 90 = 150. Eliminate (C). Choice (D) becomes 80 - 90 = -10. Eliminate (D). The correct answer is (B).