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Find the measures, in degrees, of angles GEF and DEG.
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09 Mar 2019, 11:16
09 Mar 2019, 11:16
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Question Stats:
99% (00:58) correct
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Find the measures, in degrees, of angles GEF and DEG.
#GREpracticequestion Find the measures, in degrees.jpg [ 17.84 KiB | Viewed 5503 times ]
A. 30 and 150
B. 50 and 110
C. 50 and 130
D. 90 and 170
E. 110 and 130
Attachment:
#GREpracticequestion Find the measures, in degrees.jpg [ 17.84 KiB | Viewed 5503 times ]
A. 30 and 150
B. 50 and 110
C. 50 and 130
D. 90 and 170
E. 110 and 130
Re: Find the measures, in degrees, of angles GEF and DEG.
[#permalink]
17 Mar 2019, 18:16
17 Mar 2019, 18:16
1
Expert Reply
Okay, so the angle opposite DEG will also be x + 20. Similarly, the angle opposite GEF will also be x - 60.
All four of these angles must add to 360 degrees. Hence:
(x + 20) + (x + 20) + (x - 60) + (x - 60) = 360
Combine like terms:
4x - 80 = 360
Add 80 to both sides:
4x = 440
Divide by 4:
x = 110
The two angles, then, are (110 + 20) and (110 - 60) = 130 and 50, choice C.
All four of these angles must add to 360 degrees. Hence:
(x + 20) + (x + 20) + (x - 60) + (x - 60) = 360
Combine like terms:
4x - 80 = 360
Add 80 to both sides:
4x = 440
Divide by 4:
x = 110
The two angles, then, are (110 + 20) and (110 - 60) = 130 and 50, choice C.
gmatclubot
Re: Find the measures, in degrees, of angles GEF and DEG. [#permalink]
17 Mar 2019, 18:16
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