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Which one of the following is true regarding the triangle shown in fig

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Which one of the following is true regarding the triangle shown in fig  [#permalink]

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New post 11 Oct 2018, 02:08
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Which one of the following is true regarding the triangle shown in figure?


(A) x > y > z

(B) x < y < z

(C) x = y = z

(D) \(2x = \frac{3y}{2} = z\)

(E) \(\frac{x}{2} = \frac{2y}{3} = z\)


Attachment:
triangle.jpg
triangle.jpg [ 16.93 KiB | Viewed 543 times ]

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Re: Which one of the following is true regarding the triangle shown in fig  [#permalink]

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New post 11 Oct 2018, 02:21
We know that in a triangle,angle corresponding to greater side is greater,hence angle(CAB>ACB>ABC) ---------(i)
Also we know that since vertically opposite angles are equal
angle(CAB=x)
angle(ACB=y)
angle(ABC=z) ----------------(ii)
From equation (i) & (ii)
x>y>z
Hence,answer should be A
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Re: Which one of the following is true regarding the triangle shown in fig  [#permalink]

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New post 11 Oct 2018, 07:48
Bunuel wrote:
Image
Which one of the following is true regarding the triangle shown in figure?


(A) x > y > z

(B) x < y < z

(C) x = y = z

(D) \(2x = \frac{3y}{2} = z\)

(E) \(\frac{x}{2} = \frac{2y}{3} = z\)

Attachment:
triangle.jpg


Greater the side = Greater the Angle facing it

∠BAC = x ; ∠ACB =y & ∠ABC = z

Further, we have BC > AB > AC : x > y > z ; Answer must be (A)
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Re: Which one of the following is true regarding the triangle shown in fig  [#permalink]

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New post 11 Oct 2018, 08:41
[quote="Bunuel"]Image
Which one of the following is true regarding the triangle shown in figure?


(A) x > y > z

(B) x < y < z

(C) x = y = z

(D) \(2x = \frac{3y}{2} = z\)

(E) \(\frac{x}{2} = \frac{2y}{3} = z\)

A . The Angle of a Triangle Opposite The Longest Side is the Largest Angle

So A is the answer
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Re: Which one of the following is true regarding the triangle shown in fig  [#permalink]

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New post 13 Oct 2018, 17:46
Bunuel wrote:
Image
Which one of the following is true regarding the triangle shown in figure?


(A) x > y > z

(B) x < y < z

(C) x = y = z

(D) \(2x = \frac{3y}{2} = z\)

(E) \(\frac{x}{2} = \frac{2y}{3} = z\)


Attachment:
triangle.jpg



We see that the measures of the interior angles of the triangle are angle A = x, angle B = z and angle C = y.

We see that since angle A is opposite the longest side, it’s the largest angle; since angle C is opposite the second longest side, it's the second largest angle; and, since angle B is opposite the shortest side, it’s the smallest angle.

Thus, x > y > z.

Answer: A
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Re: Which one of the following is true regarding the triangle shown in fig   [#permalink] 13 Oct 2018, 17:46
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