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# If AB||CD, what is the sum of angle ABC and angle BCD?

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Math Expert
Joined: 02 Sep 2009
Posts: 56251
If AB||CD, what is the sum of angle ABC and angle BCD?  [#permalink]

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24 Aug 2018, 05:16
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Difficulty:

25% (medium)

Question Stats:

88% (00:52) correct 13% (00:56) wrong based on 28 sessions

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If AB||CD, what is the sum of angle ABC and angle BCD?

(1) ABC is more than 80°.
(2) BCD is 90°.

Attachment:

image005.jpg [ 1.45 KiB | Viewed 490 times ]

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Re: If AB||CD, what is the sum of angle ABC and angle BCD?  [#permalink]

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24 Aug 2018, 05:20
1 is insufficient.

From 2: BCD = 90. Then ABC = 90.

BCD+ABC = 180.

B is sufficient

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If AB||CD, what is the sum of angle ABC and angle BCD?  [#permalink]

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24 Aug 2018, 06:00
Bunuel wrote:

If AB||CD, what is the sum of angle ABC and angle BCD?

(1) ABC is more than 80°.
(2) BCD is 90°.

Attachment:
image005.jpg

Given, AB || CD,
To find sum of angle ABC and angle BCD, we require the measure of any of the two angles.
Note:-(If the two lines crossed are parallel, the alternate angles are equal. Angle ABC=Angle BCD)

St1:- ABC is more than 80°.
No fixed measure of angle ABC.
Insufficient.

St2:-BCD is 90°
So, $$\angle{BCD}=\angle{ABC}=90°$$Therefore, sum of angle ABC and angle BCD can be determined.
Sufficient.

Ans. (B)
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Re: If AB||CD, what is the sum of angle ABC and angle BCD?  [#permalink]

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24 Aug 2018, 09:43

Solution

Given:
• AB is parallel to CD

To find:
• ∠ABC + ∠BCD

Approach and Working:
• Since, AB II CD, we can say that ∠ABC = ∠BCD (alternate angles of a transversal)

Analysing Statement 1
• We are given that ∠ABC > 80 degrees
o Which implies, ∠ABC + ∠BCD > 160 degrees
• So, we cannot find a unique value of ∠ABC + ∠BCD
Therefore, Statement 1 alone is not sufficient to answer this question

Analysing Statement 2
• We are given that ∠BCD = 90 degrees, implies ∠ABC = 90 degrees
• Thus, ∠ABC + ∠BCD = 180 degrees
Therefore, Statement 2 alone is sufficient to find an answer.

Hence, the correct answer is option B.

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Re: If AB||CD, what is the sum of angle ABC and angle BCD?   [#permalink] 24 Aug 2018, 09:43
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