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If the lengths of the sides of a triangle are x, x + 1 and x + 2, which of the following is a possible measure for the angle opposite the side with length x?

Re: If the lengths of the sides of a triangle are x, x + 1 and x + 2, whic [#permalink]

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24 Aug 2017, 01:34

Bunuel wrote:

If the lengths of the sides of a triangle are x, x + 1 and x + 2, which of the following is a possible measure for the angle opposite the side with length x?

(A) 58° (B) 60° (C) 61° (D) 62° (E) 89°

The angle opposite the larger side is larger. Hence, the angle opposite the side with length \(x\) is the smallest. Thus, it must be less than 60 degree. Answer A.
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Re: If the lengths of the sides of a triangle are x, x + 1 and x + 2, whic [#permalink]

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24 Aug 2017, 01:36

Bunuel wrote:

If the lengths of the sides of a triangle are x, x + 1 and x + 2, which of the following is a possible measure for the angle opposite the side with length x?

(A) 58° (B) 60° (C) 61° (D) 62° (E) 89°

if all the sides are equal then the angle will be 60..,however the other two sides are larger and hence greater than 60.Therefore angle opposite to x will be less than 60.

If the lengths of the sides of a triangle are x, x + 1 and x + 2, which of the following is a possible measure for the angle opposite the side with length x?

(A) 58° (B) 60° (C) 61° (D) 62° (E) 89°

Since x is the smallest side, the angle opposite side x must be the smallest angle. From the given answer choices, the only possibility is choice A (58 degrees). If the smallest angle were any of the other choices, say choice B (60 degrees), then each of the other two angles would be more than 60 degrees. This would make the sum of the 3 angles of the triangle more than 180 degrees, which is not possible. Thus, the smallest angle must be less than 60 degrees and the correct answer choice is A, 58 degrees.

Answer: A
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