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# What is the value of x in the figure above?

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Math Expert
Joined: 02 Sep 2009
Posts: 47037
What is the value of x in the figure above? [#permalink]

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01 Sep 2017, 00:43
00:00

Difficulty:

5% (low)

Question Stats:

97% (00:44) correct 3% (00:07) wrong based on 50 sessions

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What is the value of x in the figure above?

(A) 80
(B) 75
(C) 70
(D) 65
(E) 60

Attachment:

2017-09-01_1134.png [ 13.51 KiB | Viewed 1013 times ]

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What is the value of x in the figure above? [#permalink]

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01 Sep 2017, 08:46
1
Bunuel wrote:

What is the value of x in the figure above?

(A) 80
(B) 75
(C) 70
(D) 65
(E) 60

Attachment:
2017-09-01_1134.png

All but two of the values for angle measures in the figure are irrelevant.

Vertical angles created by the intersection of two lines are congruent.

The two missing angles for the triangle containing angle with measure $$x$$ are vertical angles with measures 50, and 55.

Sum of angles in a triangle is 180

50 + 55 + x = 180
x = 75

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Re: What is the value of x in the figure above? [#permalink]

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07 Sep 2017, 07:16
Bunuel wrote:

What is the value of x in the figure above?

(A) 80
(B) 75
(C) 70
(D) 65
(E) 60

Attachment:
2017-09-01_1134.png

We see that the other two angles in the same triangle with x are 50 and 55, and thus x is 180 - (50 + 55) = 180 - 105 = 75.

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Re: What is the value of x in the figure above? [#permalink]

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07 Sep 2017, 07:34
What is the value of x in the figure above?

(A) 80
(B) 75
(C) 70
(D) 65
(E) 60

Attachment:
2017-09-01_1134.png
[/quote]

The question tests the basic concept that : when two lines intersect, the angles formed opposite to each other at the point of intersection are equal to each other.
In the given figure, using the same concept and that of sum of interior angles of a triangle is 180 deg : x+55+50 = 180 viz. x = 75 degrees.

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Re: What is the value of x in the figure above? [#permalink]

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07 Sep 2017, 09:19
Bunuel wrote:

What is the value of x in the figure above?

(A) 80
(B) 75
(C) 70
(D) 65
(E) 60

Attachment:
2017-09-01_1134.png

We see that the two lines of triangle containing x intersect .
Therefore in the smaller triangle the 3 angles are x, 55 and 50, since in intersecting lines, opposite angles are equal.
hence, x+55+50=180
x=75 (B)

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Re: What is the value of x in the figure above?   [#permalink] 07 Sep 2017, 09:19
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