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The triangle in the figure above has two sides extended as shown. What

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The triangle in the figure above has two sides extended as shown. What [#permalink]

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New post 09 Aug 2017, 04:41
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A
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C
D
E

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The triangle in the figure above has two sides extended as shown. What is the value of x?

(A) 38
(B) 78
(C) 102
(D) 106
(E) 116

[Reveal] Spoiler:
Attachment:
2017-08-09_1259.png
2017-08-09_1259.png [ 4.57 KiB | Viewed 313 times ]
[Reveal] Spoiler: OA

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Re: The triangle in the figure above has two sides extended as shown. What [#permalink]

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New post 09 Aug 2017, 08:44
angle adjacent to \(\angle x = 180- x\) ... (i)

External angle of a triangle = sum of angles on opposite side -->

\(142 = (180-x) + 64\)

solving for x, x = 102 (Choice C)

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Re: The triangle in the figure above has two sides extended as shown. What [#permalink]

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New post 09 Aug 2017, 09:13
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Since the sum of angles in a straight line is 180,
the angle inside the triangle adjacent to 142 degree is 38 degree.
Also, the third angle in the triangle is 180 - x

180 - x + 38 + 64 = 180(Sum of angles in a triangle is 180 degree)
38 + 64 = 180 - 180 + x
x = 38 + 64 = 102(Option C)
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Re: The triangle in the figure above has two sides extended as shown. What [#permalink]

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New post 09 Aug 2017, 15:30
Exterior angle = Sum of interior opposite angles.

Hence x = 64 + (180-142) => 64+38 => 102

Hence C.
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Re: The triangle in the figure above has two sides extended as shown. What   [#permalink] 09 Aug 2017, 15:30
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