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

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Math Expert
Joined: 02 Sep 2009
Posts: 58335
In the diagram, ℓ1 is parallel to ℓ2. The measure of ∠ a is 40 degrees  [#permalink]

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21 Dec 2018, 02:48
00:00

Difficulty:

15% (low)

Question Stats:

91% (01:42) correct 9% (00:26) wrong based on 29 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 [ 14.19 KiB | Viewed 326 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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21 Dec 2018, 03:47
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:

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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Joined: 04 Jan 2015
Posts: 3074
In the diagram, ℓ1 is parallel to ℓ2. The measure of ∠ a is 40 degrees  [#permalink]

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21 Dec 2018, 05:40

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

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In the diagram, ℓ1 is parallel to ℓ2. The measure of ∠ a is 40 degrees   [#permalink] 21 Dec 2018, 05:40
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