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Sub 505 (Easy)|   Geometry|      
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Bunuel
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If y = 2x, and x = z/3, what is v = ? 01 Aug 2017, 04:41
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C
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97% (01:02) correct 3% (00:21) wrong based on 43 sessions

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If y = 2x, and x = z/3, what is v = ?

(A) 30°
(B) 45°
(C) 60°
(D) 75°
(E) 90°


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C
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If y = 2x, and x = z/3, what is v = ? 01 Aug 2017, 04:55
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Since x = z/3, we can say that z = 3x
We already know that y=2x

Sum of angles in a straight line is 180 degree
x + 2x + 3x = 180° => x = 30°
Since y = 2x, y =60°

Angle v and y are alternate angles and are hence, equal
Therefore, v = 60°(Option C)
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If y = 2x, and x = z/3, what is v = ? 01 Aug 2017, 07:59
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Bunuel

If y = 2x, and x = z/3, what is v = ?

(A) 30°
(B) 45°
(C) 60°
(D) 75°
(E) 90°


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2017-08-01_1348.png
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Here from figure v=Y
x+y+z=180
putting values from question stem
x+2x+3x=180 => 6x=180=> x=30 hence y=60
so v =60
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If y = 2x, and x = z/3, what is v = ? 02 Aug 2017, 13:37
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Bunuel

If y = 2x, and x = z/3, what is v = ?

(A) 30°
(B) 45°
(C) 60°
(D) 75°
(E) 90°


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Attachment:
2017-08-01_1348.png
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We see that:

x + y + z + x + v + z = 360

and

y = v

We are also given that:

y = 2x

and

x = z/3 or z = 3x

Thus, we can get all of our variables in terms of x:

y = 2x, z = 3x, v = 2x; thus:

x + 2x + 3x + x + 2x + 3x = 360

12x = 360

x = 30

Since x = 30, v = 60.

Answer: C
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