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# In ∆ ABC above, if DE is parallel to AC, then x =

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Math Expert
Joined: 02 Sep 2009
Posts: 55277
In ∆ ABC above, if DE is parallel to AC, then x =  [#permalink]

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24 Aug 2017, 23:51
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Difficulty:

35% (medium)

Question Stats:

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

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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 928 times ]

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

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25 Aug 2017, 00:15

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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25 Aug 2017, 11:02
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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Re: In ∆ ABC above, if DE is parallel to AC, then x =  [#permalink]

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26 Aug 2017, 19:34
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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29 Aug 2017, 17:24
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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Re: In ∆ ABC above, if DE is parallel to AC, then x =   [#permalink] 29 Aug 2017, 17:24
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# In ∆ ABC above, if DE is parallel to AC, then x =

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