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505-555 (Easy)|   Geometry|      
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Bunuel
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In ∆ ABC above, if DE is parallel to AC, then x = 24 Aug 2017, 23:51
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15% (low)

Question Stats:

77% (01:18) correct 23% (02:18) wrong based on 107 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

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2017-08-25_1042_001.png
2017-08-25_1042_001.png [ 16.45 KiB | Viewed 3941 times ]
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E
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In ∆ ABC above, if DE is parallel to AC, then x = 25 Aug 2017, 00:15
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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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In ∆ ABC above, if DE is parallel to AC, then x = 25 Aug 2017, 11:02
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Bunuel

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

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

Show Spoiler
Attachment:
2017-08-25_1042_001.png
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- 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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In ∆ ABC above, if DE is parallel to AC, then x = 26 Aug 2017, 19:34
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Bunuel

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

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

Show Spoiler
Attachment:
2017-08-25_1042_001.png
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Sum of angles in ∆ ABC =180

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

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

Answer: E
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In ∆ ABC above, if DE is parallel to AC, then x = 29 Aug 2017, 17:24
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Bunuel

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

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

Show Spoiler
Attachment:
2017-08-25_1042_001.png
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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.

Answer: E
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In ∆ ABC above, if DE is parallel to AC, then x = 28 Jul 2020, 11:03
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