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In the figure above, x =

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

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New post 08 Aug 2017, 10:15
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A
B
C
D
E

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(N/A)

Question Stats:

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

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Re: In the figure above, x = [#permalink]

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New post 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.
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Re: In the figure above, x = [#permalink]

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New post 08 Aug 2017, 10:24
Bunuel wrote:
Image
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.
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Re: In the figure above, x = [#permalink]

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New post 08 Aug 2017, 10:30
Bunuel wrote:
Image
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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New post 08 Aug 2017, 12:21
Bunuel wrote:
Image
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 \(180^{\circ}\).

\(z + x = 180\)

\(60 + x = 180\)

\(x = 180 - 60 => 120\)

Answer (B)...
In the figure above, x =   [#permalink] 08 Aug 2017, 12:21
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