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555-605 (Medium)|   Geometry|      
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Bunuel
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In the figure below, ∠ADE = 60°, ∠EFC = 40°, and ∠DAE = 55°. If AB || 20 Mar 2015, 07:13
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35% (medium)

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74% (02:13) correct 26% (02:37) wrong based on 292 sessions

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Attachment:
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originals (1).jpg [ 16.12 KiB | Viewed 12542 times ]
In the figure below, ∠ADE = 60°, ∠EFC = 40°, and ∠DAE = 55°. 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

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A
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hsbinfy
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In the figure below, ∠ADE = 60°, ∠EFC = 40°, and ∠DAE = 55°. If AB || 20 Mar 2015, 12:31
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its A =75

angle AED=65 (AED is 180) =angle FEC( opp)

thru above FCE =75 which makes ECB=115 again

EAB =65(vertically opp angles thru thr trnsversal between the parallel lines)
now we have all four angles of quad ABCE

so we can solve x=75
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In the figure below, ∠ADE = 60°, ∠EFC = 40°, and ∠DAE = 55°. If AB || 20 Mar 2015, 20:35
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Bunuel
Attachment:
originals (1).jpg
In the figure below, ∠ADE = 60°, ∠EFC = 40°, and ∠DAE = 55°. 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

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It looks to me that triangles ABF and ECF are similar triangles.
If that is the case then angle AED is 65 (found by 180-55-60=65)
Angle CEF is a vertical angle so it also equals 65.
Finally this leads us to angle ECF which is 75 (found by 180-65-40=75)

x= 75

Answer: A
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In the figure below, ∠ADE = 60°, ∠EFC = 40°, and ∠DAE = 55°. If AB || 23 Mar 2015, 00:29
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Answer = A = 75

Refer diagram below:

Attachment:
originals%20(1).jpg
originals%20(1).jpg [ 20.85 KiB | Viewed 11362 times ]

\(\angle ABC = \angle ECF = x\) (They are alternate angles)

x = 180-(75+40) = 75
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In the figure below, ∠ADE = 60°, ∠EFC = 40°, and ∠DAE = 55°. If AB || 23 Mar 2015, 05:43
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Bunuel

In the figure below, ∠ADE = 60°, ∠EFC = 40°, and ∠DAE = 55°. 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

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MAGOOSH OFFICIAL SOLUTION:
Attachment:
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In the figure below, ∠ADE = 60°, ∠EFC = 40°, and ∠DAE = 55°. If AB || 23 Mar 2015, 11:14
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Bunuel
Attachment:
originals (1).jpg
In the figure below, ∠ADE = 60°, ∠EFC = 40°, and ∠DAE = 55°. 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

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Answer is A: 75.

Number of properties come into play.
First, sum of angles in a triangle is 180. That gives us value of \(<AED = 65.\)
Second, Vertically opposite angles are equal, gives us \(<AED = <CEF = 65\).
Again, angle sum property of a Triangle gives \(<ECF = 75\)

Third, Linear pair, gives \(< BCD = 105\)

Fourth, Sum of angles on the same side of transversal BC (AB parallel CD) is supplementary, gives \(<ABC=x=75\).

Thank you.
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In the figure below, ∠ADE = 60°, ∠EFC = 40°, and ∠DAE = 55°. If AB || 25 Mar 2016, 08:37
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Bunuel
Attachment:
originals (1).jpg
In the figure below, ∠ADE = 60°, ∠EFC = 40°, and ∠DAE = 55°. 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

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AED=CEF=65 deg

ECF=75 deg

ECF=ABC (Corresponding angles)
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In the figure below, ∠ADE = 60°, ∠EFC = 40°, and ∠DAE = 55°. If AB || 25 May 2025, 11:58
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