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In the figure above, side AB is parallel to side DE, and the measure

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In the figure above, side AB is parallel to side DE, and the measure  [#permalink]

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New post 29 Aug 2018, 01:58
1
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A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

79% (01:59) correct 21% (02:22) wrong based on 80 sessions

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In the figure above, side AB is parallel to side DE, and the measure of angle D is 40% that of angle E, what is the value of angle A?

A. 20
B. 26
C. 44
D. 46
E. 110


Spoiler: ::
Attachment:
image001 (1).gif
image001 (1).gif [ 851 Bytes | Viewed 1055 times ]
Spoiler: OA

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Re: In the figure above, side AB is parallel to side DE, and the measure  [#permalink]

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New post 29 Aug 2018, 02:01
Angle E = Angle B = 110
angle d = 0.4*110 = 44
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In the figure above, side AB is parallel to side DE, and the measure  [#permalink]

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New post 29 Aug 2018, 02:18
pandeyashwin wrote:
Angle E = Angle B = 110
angle d = 0.4*110 = 44


Pandey Ji we need angle A

angle A = angle D = 44 (alternate angle)

or

angle ABC = angle DEC (alternate angle) = 110
angle D = 44
angle ECD = 180 -(110+44) = 26 = angle ACB (vertically opposite)
angle A = 180-(110+26) = 44
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Re: In the figure above, side AB is parallel to side DE, and the measure  [#permalink]

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New post 29 Aug 2018, 05:03
Angle B = Angle E = 110

Angle D = 40% of 110 = 44

Angle C = 180 - ( 110 + 44 ) = 26

Angle A = 180 - ( 110 + 26 ) = 44

Hence, C.
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Re: In the figure above, side AB is parallel to side DE, and the measure  [#permalink]

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New post 29 Aug 2018, 16:06
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Top Contributor
Bunuel wrote:
Image
In the figure above, side AB is parallel to side DE, and the measure of angle D is 40% that of angle E, what is the value of angle A?

A. 20
B. 26
C. 44
D. 46
E. 110


Spoiler: ::
Attachment:
image001 (1).gif


Since we have some parallel lines, there are several pairs of equal angles in this diagram.
Image

First of all, ∠E = ∠B. So, ∠E = 110°
Image

Next, since ∠D = 40% of ∠E, we now know that ∠D = 40% of 110%
So, ∠D = 44%
Image

Finally, ∠A = ∠D. So, ∠A = 44°

Answer: D

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Re: In the figure above, side AB is parallel to side DE, and the measure   [#permalink] 29 Aug 2018, 16:06
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