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In a triangle ABC, BC is produced to D and bisectors of angle ABC and

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In a triangle ABC, BC is produced to D and bisectors of angle ABC and  [#permalink]

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New post 17 Nov 2018, 10:21
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A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

21% (02:41) correct 79% (03:02) wrong based on 39 sessions

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GMATbuster's Weekly Quant Quiz#9 Ques 9


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In a triangle ABC, BC is produced to D and bisectors of angle ABC and angle ACD meet at E. Is Angle BEC <30 deg?
1) Angle BAC = 60 deg
2) Angle BCA = 40 deg

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Re: In a triangle ABC, BC is produced to D and bisectors of angle ABC and  [#permalink]

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New post 17 Nov 2018, 10:32
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Let ABE = EBC = x, and ACE = ECD = y

Stmt 1: BAC = 60, 2x + 60 = 2y using exterior angle property or x + 30 = y which gives, Angle BEC = 30 deg. Hence answer is always NO. Hence Sufficient!

Stmt 2: BCA = 40, so ACD = 140 = 2y which gives y = 70, Also, EBC + 40 + ACE + BEC = 180, hence, x + 40 + 70 + BEC = 180, or BEC = 180 - 110 - x = 70 - x.
Now, y = 70, so, BEC = y - x, cannot proceed further on this without more details. Hence, Insufficient.

Hence Option A
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Re: In a triangle ABC, BC is produced to D and bisectors of angle ABC and  [#permalink]

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New post 17 Nov 2018, 11:19
A) Does not give any information on any other angle. Not sufficient
B)If angle BCA=40, then angle ACD=140
angle ACE=70
So, angle BCE=110
Angle ABC+ Angle BAC= angle ACD=140
But, angle BEC can be greater or lesser than 30. Not sufficient
combine:
angle BCE=110
Angle ABC=140-60=80
Angle EBC=40
So, Angle BEC=180-(110+40)
Sufficient
IMO:OPTION C
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Re: In a triangle ABC, BC is produced to D and bisectors of angle ABC and  [#permalink]

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New post 07 Mar 2019, 01:58
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gmatbusters
Question says, bisector of angle BCD and the figure bisects angle ACD.

Going as per question, answer must be option C.
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Re: In a triangle ABC, BC is produced to D and bisectors of angle ABC and  [#permalink]

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New post 07 Mar 2019, 02:24
Thanks for pointing out the typo.

The angle ACD is bisected and not the angle BCD.

The typo is removed.

MittalMewada wrote:
gmatbusters
Question says, bisector of angle BCD and the figure bisects angle ACD.

Going as per question, answer must be option C.


Posted from my mobile device
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Re: In a triangle ABC, BC is produced to D and bisectors of angle ABC and  [#permalink]

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New post 30 Mar 2019, 07:13
nkin wrote:
Let ABE = EBC = x, and ACE = ECD = y

Stmt 1: BAC = 60, 2x + 60 = 2y using exterior angle property or x + 30 = y which gives, Angle BEC = 30 deg. Hence answer is always NO. Hence Sufficient!

Stmt 2: BCA = 40, so ACD = 140 = 2y which gives y = 70, Also, EBC + 40 + ACE + BEC = 180, hence, x + 40 + 70 + BEC = 180, or BEC = 180 - 110 - x = 70 - x.
Now, y = 70, so, BEC = y - x, cannot proceed further on this without more details. Hence, Insufficient.

Hence Option A


How did you get 2x+60 =2y .

Could you please show diagramatically
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Re: In a triangle ABC, BC is produced to D and bisectors of angle ABC and   [#permalink] 30 Mar 2019, 07:13
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