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In the diagram, ℓ1 is parallel to ℓ2. The measure of ∠ a is 40 degrees

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In the diagram, ℓ1 is parallel to ℓ2. The measure of ∠ a is 40 degrees  [#permalink]

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New post 21 Dec 2018, 01:48
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88% (01:26) correct 12% (00:10) wrong based on 26 sessions

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In the diagram, ℓ1 is parallel to ℓ2. The measure of ∠a is 40 degrees. What is the sum of the measures of angles d and w less the sum of the measures of angles y and c?


A. 50
B. 80
C. 90
D. 100
E. 120

Attachment:
lines.jpg
lines.jpg [ 14.19 KiB | Viewed 222 times ]

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Re: In the diagram, ℓ1 is parallel to ℓ2. The measure of ∠ a is 40 degrees  [#permalink]

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New post 21 Dec 2018, 02:47
a=40, b= 140

d,y,w,b=140 and a,c,z,x= 40

so d+w= 140+140= 280 and y+c= 140+40= 180

280-180 = 100 IMO D


Bunuel wrote:
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In the diagram, ℓ1 is parallel to ℓ2. The measure of ∠a is 40 degrees. What is the sum of the measures of angles d and w less the sum of the measures of angles y and c?


A. 50
B. 80
C. 90
D. 100
E. 120

Attachment:
lines.jpg

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In the diagram, ℓ1 is parallel to ℓ2. The measure of ∠ a is 40 degrees  [#permalink]

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New post 21 Dec 2018, 04:40

Solution


Given:
    • \(l_1\) is parallel to \(l_2\)
    • ∠a = 40

To find:
    • ∠d + ∠w – (∠y + ∠c)

Approach and Working:
    • ∠d = ∠y (alternate angles)
    • ∠a = ∠c = 40 (opposite angles)
    • ∠w = 180 - ∠c = 140 (corresponding angles sum = 180)

Thus, ∠d + ∠w – (∠y + ∠c) = ∠d - ∠y + 140 – 40 = 100

Hence, the correct answer is Option D

Answer: D

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In the diagram, ℓ1 is parallel to ℓ2. The measure of ∠ a is 40 degrees &nbs [#permalink] 21 Dec 2018, 04:40
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In the diagram, ℓ1 is parallel to ℓ2. The measure of ∠ a is 40 degrees

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