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Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  In ∆ ABC above, if DE is parallel to AC, then x =

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Math Expert V
Joined: 02 Sep 2009
Posts: 55729
In ∆ ABC above, if DE is parallel to AC, then x =  [#permalink]

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1 00:00

Difficulty:   35% (medium)

Question Stats: 84% (01:15) correct 16% (02:23) wrong based on 63 sessions

HideShow timer Statistics In ∆ ABC above, if DE is parallel to AC, then x =

(A) 70
(B) 50
(C) 40
(D) 30
(E) 20

Attachment: 2017-08-25_1042_001.png [ 16.45 KiB | Viewed 942 times ]

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Re: In ∆ ABC above, if DE is parallel to AC, then x =  [#permalink]

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1
Bunuel wrote: In ∆ ABC above, if DE is parallel to AC, then x =

(A) 70
(B) 50
(C) 40
(D) 30
(E) 20

Attachment:
2017-08-25_1042_001.png

- Because DE parallel with AC, so X must be equal with y --> alternate angles.
- So, if we know Y, we know X (X=Y).
- From triangle ABC = 180-2Y-80-60=0 --> 2Y=40, Y=20.
- Thus X=20.

E.
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Senior PS Moderator V
Joined: 26 Feb 2016
Posts: 3372
Location: India
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Re: In ∆ ABC above, if DE is parallel to AC, then x =  [#permalink]

Show Tags Since DE is parallel to AC, Angle BDE = 60(corresponding angles)
Also, the third angle in the triangle is 180 - (60 + 80) = 40
Angle EDA = 180 - 40 = 140(Angles in a straight line sum to 180)

2y = 40(corresponding angles) => y = 20
In ∆EDA, x + y + 140 = 180
Therefore, x = 180 - 140 - 20 = 20(Option E)
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Re: In ∆ ABC above, if DE is parallel to AC, then x =  [#permalink]

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Bunuel wrote: In ∆ ABC above, if DE is parallel to AC, then x =

(A) 70
(B) 50
(C) 40
(D) 30
(E) 20

Attachment:
2017-08-25_1042_001.png

Sum of angles in ∆ ABC =180

2y = 180 - 80 - 60 = 40..........y = 20

DE is parallel to AC......then y =x =20

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Re: In ∆ ABC above, if DE is parallel to AC, then x =  [#permalink]

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Bunuel wrote: In ∆ ABC above, if DE is parallel to AC, then x =

(A) 70
(B) 50
(C) 40
(D) 30
(E) 20

Attachment:
2017-08-25_1042_001.png

Because angles x and y are alternate interior angles, we see that angle x = angle y.

For triangle ABC, we can create the following equation:

80 + 60 + 2y = 180

2y = 40

y = 20

So x = 20.

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If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: In ∆ ABC above, if DE is parallel to AC, then x =   [#permalink] 29 Aug 2017, 17:24
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