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If AB||CD, what is the value of x?

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Math Expert

Joined: 02 Sep 2009

Posts: 58320

If AB||CD, what is the value of x? [#permalink]

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07 Feb 2019, 07:46

00:00

Difficulty:

55% (hard)

Question Stats:

64% (02:16) correct

36% (02:21) wrong

based on 42 sessions

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If AB||CD, what is the value of x?

Note: Figure not drawn to scale

A. 75
B. 85
C. 95
D. 105
E. 115

Spoiler: ::

Attachment:

Geometry_009.jpg [ 22.73 KiB | Viewed 770 times ]

Spoiler: OA

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Joined: 09 May 2018

Posts: 6

Re: If AB||CD, what is the value of x? [#permalink]

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07 Feb 2019, 08:47

Angle EAB= 180 - (Angle DAE + Angle ADE
Angle EAB= 180 - (55+60)
Angle EAB= 65 (Property of a Quad.)

Angle EAB = Angle FAB = 65

Angle FAB + Angle AFB + Angle ABF = 180
65+40+ Angle ABF =180
Angle AFB= 180-105
Angle AFB=75

Hence answer is (A)

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Manager

Joined: 27 Jun 2015

Posts: 54

GRE 1: Q158 V143

Re: If AB||CD, what is the value of x? [#permalink]

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07 Feb 2019, 08:49

As per the figure AB is parellel to DC then angle bac will be 65 degree.
Then in triangle BAF angle B will be 75 degree

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Re: If AB||CD, what is the value of x? [#permalink]

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07 Feb 2019, 10:20

Bunuel wrote:

If AB||CD, what is the value of x?

Note: Figure not drawn to scale

A. 75
B. 85
C. 95
D. 105
E. 115

Spoiler: ::

Attachment:

The attachment Geometry_009.jpg is no longer available

Solution attached
IMO A

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IMG_20190207_224923075.jpg [ 3.25 MiB | Viewed 571 times ]

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Re: If AB||CD, what is the value of x? [#permalink]

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10 Feb 2019, 08:34

Bunuel wrote:

If AB||CD, what is the value of x?

Note: Figure not drawn to scale

A. 75
B. 85
C. 95
D. 105
E. 115

Spoiler: ::

Attachment:

Geometry_009.jpg

Since AB || CD, then angle ABC = angle ECF. So angle ECF = x. We see that angle AED = 180 - 55 - 60 = 65, and since angles AED and CEF are vertical angles, angle CEF = 65. Therefore, using triangle CEF, we have:

x + 65 + 40 = 180

x + 105 = 180

x = 75

Answer: A
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