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

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

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New post 24 Aug 2018, 05:16
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A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

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

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

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New post 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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New post 24 Aug 2018, 06:00
Bunuel wrote:
Image
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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New post 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.

Answer: 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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