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In the figure below, ∠ADE = 60°, ∠EFC = 40°, and ∠DAE = 55°. If AB  [#permalink]
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20 Mar 2015, 06:13
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Re: In the figure below, ∠ADE = 60°, ∠EFC = 40°, and ∠DAE = 55°. If AB  [#permalink]
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20 Mar 2015, 11:31
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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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Re: In the figure below, ∠ADE = 60°, ∠EFC = 40°, and ∠DAE = 55°. If AB  [#permalink]
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20 Mar 2015, 19:35
Bunuel wrote: 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 Kudos for a correct solution.It looks to me that triangles ABF and ECF are similar triangles. If that is the case then angle AED is 65 (found by 1805560=65) Angle CEF is a vertical angle so it also equals 65. Finally this leads us to angle ECF which is 75 (found by 1806540=75) x= 75 Answer: A



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figure below, ∠ADE = 60°, ∠EFC = 40°, and ∠DAE = 55°. If AB  [#permalink]
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22 Mar 2015, 23:29
Answer = A = 75 Refer diagram below: Attachment:
originals%20(1).jpg [ 20.85 KiB  Viewed 2360 times ]
\(\angle ABC = \angle ECF = x\) (They are alternate angles) x = 180(75+40) = 75
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Re: In the figure below, ∠ADE = 60°, ∠EFC = 40°, and ∠DAE = 55°. If AB  [#permalink]
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23 Mar 2015, 04:43



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Re: In the figure below, ∠ADE = 60°, ∠EFC = 40°, and ∠DAE = 55°. If AB  [#permalink]
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23 Mar 2015, 10:14
Bunuel wrote: 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 Kudos for a correct solution.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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Re: In the figure below, ∠ADE = 60°, ∠EFC = 40°, and ∠DAE = 55°. If AB  [#permalink]
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25 Mar 2016, 07:37
Bunuel wrote: 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 Kudos for a correct solution.AED=CEF=65 deg ECF=75 deg ECF=ABC (Corresponding angles)



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Re: In the figure below, ∠ADE = 60°, ∠EFC = 40°, and ∠DAE = 55°. If AB  [#permalink]
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14 Aug 2017, 04:22
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Re: In the figure below, ∠ADE = 60°, ∠EFC = 40°, and ∠DAE = 55°. If AB 
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