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

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Math Expert
Joined: 02 Sep 2009
Posts: 43363
The triangle in the figure above has two sides extended as shown. What [#permalink]

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09 Aug 2017, 03:41
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Difficulty:

25% (medium)

Question Stats:

93% (00:23) correct 7% (00:00) wrong based on 36 sessions

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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 [ 4.57 KiB | Viewed 547 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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09 Aug 2017, 07:44
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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09 Aug 2017, 08:13

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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09 Aug 2017, 14:30
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, 14:30
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