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M70-11

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Math Expert
Joined: 02 Sep 2009
Posts: 52296

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03 Sep 2018, 02:36
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100% (00:23) correct 0% (00:00) wrong based on 2 sessions

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In the figure above, ∠ABC equals

A. $$180 – x – y$$
B. $$x - y$$
C. $$y-x$$
D. $$180 – y+x$$
E. $$y +x$$

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Math Expert
Joined: 02 Sep 2009
Posts: 52296

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03 Sep 2018, 02:36
Official Solution:

In the figure above, ∠ABC equals

A. $$180 – x – y$$
B. $$x - y$$
C. $$y-x$$
D. $$180 – y+x$$
E. $$y +x$$

We’ll go for ALTERNATIVE because variables in all of the answers.

We can just pick any values for x and y, and see which answers fit what we get. It is better to start checking the answers to see that they do not give similar results. Say we pick x = 10 and y = 120. We get: (A) 180 – 10 – 120 = 50; (B) 10 – 120 = –110; (C) 120 – 10 = 110; (D) 180 – 120 + 10 = 70; and (E) 120 + 10 = 130. Great – all answers are different from one another. Going back to the question, since y is and exterior angle, it equals the sum of the two angles in the triangle that are not adjacent to it. Using our numbers we’ll get: 120 = ∠ACB + 10, so ∠ACB = 110. We already know than answer (C) is the only one that equals 110.

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Re M70-11 &nbs [#permalink] 03 Sep 2018, 02:36
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