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

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

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17 Nov 2018, 10:21
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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

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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17 Nov 2018, 10:32
1
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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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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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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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.

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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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 .

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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