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25 Jun 2018, 05:19
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
5%
(low)
Question Stats:
95% (01:00) correct
5%
(01:14)
wrong
based on 2549
sessions
History
Date
Time
Result
Not Attempted Yet
In the figure shown, what is the value of x ?
A. 60
B. 80
C. 85
D. 90
E. 95
NEW question from GMAT® Official Guide 2019
(PS00534)
Attachment:
PS00534_f006.jpg [ 33.29 KiB | Viewed 40799 times ]
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25 Jun 2018, 07:44
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Bunuel
See the attached figure..
Since exterior angles are 150, interior angles will be 180-150=30..
\(\angle ABC = \angle BAC = \angle DEC = 180-150=30\)
Therefore the third angle, \(\angle BCA\), in the \(\triangle ABC =180-30-30=120\)..
So adjoining angle, \(\angle BCE = 180-\angle ABC = 180-120=60\)..
Take \(\triangle CDE\) :
Sum of all angles = 180 => \(x+60+30=180\)..
\(x=90\)
D
Attachments
PicsArt_06-25-08.11.54.jpg [ 9.18 KiB | Viewed 20272 times ]
General Discussion
25 Jun 2018, 05:34
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Solution
To find:
- • The value of the angle x, in the given figure
Approach and Working:
We name the points of the diagram as follows, for our convenience of solving:
- • Now, angle ACD = 180 – 150 = 30
• Similarly, angle CAB = 180 – 150 = 30
If we consider triangle ABC, CBE is an external angle
- • Hence, angle CBE = ACD + CAB = 30 + 30 = 60
Now, considering triangle BDE,
- • Angle DBE = angle CBE = 60
• Angle DEB = 180 – 150 = 30
• Therefore, angle BDE = x = 180 – (60 + 30) = 180 – 90 = 90
Hence, the correct answer is option D.
Answer: D
