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In the figure above, what is the value of x ?

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Bunuel
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In the figure above, what is the value of x ? [#permalink] New post  22 May 2020, 03:40
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In the figure above, what is the value of x ?

A. 50
B. 70
C. 80
D. 90
E. 100


PS21152


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Re: In the figure above, what is the value of x ? [#permalink] New post  22 May 2020, 04:45
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Bunuel wrote:

In the figure above, what is the value of x ?

A. 50
B. 70
C. 80
D. 90
E. 100


PS21152


Show Spoiler
Attachment:
21152-0.png


\((n-2)*180= \)
\((4-2)*180= 360\)

\(360 - 260 = 100\)

\(100+x°=180\)
\(x=80\)

Answer C
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BrentGMATPrepNow
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Re: In the figure above, what is the value of x ? [#permalink] New post  22 May 2020, 05:05
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Bunuel wrote:

In the figure above, what is the value of x ?

A. 50
B. 70
C. 80
D. 90
E. 100
Show Spoiler
Attachment:
21152-0.png


Since angles in a quadrilateral must add to 360°, we know that the missing angle = 100°


Next, since angles on a line must add to 180°, we can write: 100° + x° = 180
Solve to get: x° = 80

Answer: C

Cheers,
Brent
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GMATWhizTeam
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Re: In the figure above, what is the value of x ? [#permalink] New post  22 May 2020, 05:16
Expert Reply
Bunuel wrote:

In the figure above, what is the value of x ?

A. 50
B. 70
C. 80
D. 90
E. 100


PS21152


Solution


    • Let us assume that the remaining one interior angle of the quadrilateral measures y degrees, as shown in the below figure.

    • Also, we know that the sum of all the interior angles of a quadrilateral \(= 360°\)
      o \(50° + 120° + 90° + y° = 360° ⟹ y° =100°\)
    • Since, x and y are straight angles,
      o So, \(x° + y° = 180° ⟹ x° + 100° = 180° ⟹ x° = 80°\)
Thus, the correct answer is Option C.
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Re: In the figure above, what is the value of x ? [#permalink] New post  15 Nov 2023, 19:22
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Re: In the figure above, what is the value of x ? [#permalink]
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