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Geometry: Parallel lines

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Geometry: Parallel lines

by ikaplan » Tue Nov 08, 2011 9:49 am
If AB || CD, what is the value of x? (please see the attached picture)

(A) 75
(B) 85
(C) 95
(D) 105
(E) 115

Source: BTG Practice questions

OA is A

What confuses me is the following: if AB || CD then angle BAD is equal to angle ADC; so, angle BAE is 5 degrees (60-55). Angle AED is 65 and CEF is 65 as well. Therefore, angle EFC is 75 degrees (as is x).

Angle CEA is 115 (180-65) and angle ECB is 105 (180-75).

If so, how come the sum of all angles of the polygon ABEC is not 360 degrees but 300 degrees?
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by gmatclubmember » Tue Nov 08, 2011 9:54 am
ikaplan wrote:If AB || CD, what is the value of x? (please see the attached picture)

(A) 75
(B) 85
(C) 95
(D) 105
(E) 115

Source: BTG Practice questions

OA is A

What confuses me is the following: if AB || Bc then angle BAD is equal to angle ADC; so, angle BAE is 5 degrees (60-55). Angle AED is 65 and CEF is 65 as well. Therefore, angle EFC is 75 degrees (as is x).

Angle CEA is 115 (180-65) and angle ECB is 105 (180-75).

If so, how come the sum of all angles of the polygon ABEC is not 360 degrees but 300 degrees?
The correct answer is 75 degrees.
And AB is || to CD and not to (BC) as you stated.
Besides the angle BAD and ADC summation would be 180 (they wont be equal).
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by user123321 » Tue Nov 08, 2011 9:57 am
since AB parallel to CD. AD is like a transversal
and sum of DAB + ADC = 180
=> DAB = 120 = DAF+FAB = 55 + FAB
=> FAB = 65

x+40+65 = 180 (because in a triangle sum of angles is 180)
x = 75 degrees

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by amit2k9 » Tue Nov 08, 2011 10:00 am
ikaplan wrote:
What confuses me is the following: if AB || Bc then angle BAD is equal to angle ADC; so, angle BAE is 5 degrees (60-55).
Interior angles on the same side of transversal are not equal but supplementary.
simple method is,
angle ABC = DCF= x
angle AED = CEF = 180-(60+55)

thus in triangle FEC,
x = 180 - [180-(60+55)+40] = 75
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by neelgandham » Tue Nov 08, 2011 10:18 am
What confuses me is the following: if AB || CD then angle BAD is equal to angle ADC; so, angle BAE is 5 degrees (60-55). Angle AED is 65 and CEF is 65 as well. Therefore, angle EFC is 75 degrees (as is x).
If so, how come the sum of all angles of the polygon ABEC is not 360 degrees but 300 degrees?
Hello ikaplan,

Now that the main question has already been answered , I will take the opportunity to answer your question. Angle BAD is NOT equal to angle ADC. Infact, Sum of Angle BAD and Angle ADC is 180 degrees (Consecutive Interior angles add up to 180 degrees). I hope that answers your question.

Let me know if you need any further clarification
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by MBA.Aspirant » Thu Nov 10, 2011 12:40 pm
A) 75
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