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Math Expert V
Joined: 02 Sep 2009
Posts: 64322

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Difficulty:   25% (medium)

Question Stats: 71% (00:27) correct 29% (01:29) wrong based on 7 sessions

### HideShow timer Statistics 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 V
Joined: 02 Sep 2009
Posts: 64322

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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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Intern  B
Joined: 30 Oct 2019
Posts: 1

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Why is the explanation solving for angle ACB?
Intern  Joined: 25 Mar 2020
Posts: 3

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Same question! I think they just they meant to type ABC Re: M70-11   [#permalink] 07 Apr 2020, 14:09

# M70-11

Moderators: chetan2u, Bunuel  