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# In the figure above, x =

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Math Expert
Joined: 02 Sep 2009
Posts: 46991
In the figure above, x = [#permalink]

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08 Aug 2017, 10:15
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Question Stats:

90% (00:07) correct 10% (00:16) wrong based on 19 sessions

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In the figure above, x =

(A) 100
(B) 120
(C) 130
(D) 140
(E) 160

Attachment:

2017-08-08_2111.png [ 4.73 KiB | Viewed 533 times ]

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Joined: 11 Jun 2017
Posts: 10
Re: In the figure above, x = [#permalink]

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08 Aug 2017, 10:21
B. 120. the reason is :- 1) sum of linear pair of angles is 180, and 2) sum of the angles of a triangle is 180.
Manager
Joined: 03 May 2017
Posts: 108
Re: In the figure above, x = [#permalink]

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08 Aug 2017, 10:24
Bunuel wrote:

In the figure above, x =

(A) 100
(B) 120
(C) 130
(D) 140
(E) 160

Attachment:
2017-08-08_2111.png

180-100= 80 gives the second angle of the triangle. 40+80= 120= Exterior angle, hence B

OR

We know the third angle on the line is 60, hence the complimentary exterior angle would be 120. Hence, B.
Senior Manager
Joined: 09 Mar 2017
Posts: 443
Location: India
Concentration: Marketing, Organizational Behavior
WE: Information Technology (Computer Software)
Re: In the figure above, x = [#permalink]

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08 Aug 2017, 10:30
Bunuel wrote:

In the figure above, x =

(A) 100
(B) 120
(C) 130
(D) 140
(E) 160

Attachment:
2017-08-08_2111.png

IMO B-120.
100 degrees = 40deg +(180-x)deg
x= 120 degrees.
Primary rule used : External angle of a triangle is equal to the sum of its two opposite internal angles.
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In the figure above, x = [#permalink]

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08 Aug 2017, 12:21
Bunuel wrote:

In the figure above, x =

(A) 100
(B) 120
(C) 130
(D) 140
(E) 160

Attachment:
2017-08-08_2111.png

Let the unknown angles inside the triangle be $$y$$ and $$z$$.

$$y + z + 40 = 180$$ -------- (i)

Straight line has angles from left to right $$100^{\circ}$$, $$y^{\circ}$$ , $$z^{\circ}$$ and $$x^{\circ}$$ respectively.

Straight line has angle equal to $$180^{\circ}$$.

$$100 + y = 180$$

$$y = 180 - 100 => 80$$

Substituting value of $$y$$ in (i), we get;

$$80 + z + 40 = 180$$

$$120 + z = 180$$

$$z = 180 - 120 => 60$$

Straight line has angle equal to $$180^{\circ}$$.

$$z + x = 180$$

$$60 + x = 180$$

$$x = 180 - 60 => 120$$

In the figure above, x =   [#permalink] 08 Aug 2017, 12:21
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