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# If CD is a bisector in triangle ABC, what is ∠ABC?

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Math Expert
Joined: 02 Sep 2009
Posts: 58434
If CD is a bisector in triangle ABC, what is ∠ABC?  [#permalink]

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16 Nov 2016, 04:50
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45% (medium)

Question Stats:

73% (01:49) correct 27% (01:52) wrong based on 197 sessions

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If CD is a bisector in triangle ABC, what is ∠ABC?

A. 25°
B. 30°
C. 35°
D. 40°
E. 45°

Attachment:

T89000.png [ 7.37 KiB | Viewed 2328 times ]

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If CD is a bisector in triangle ABC, what is ∠ABC?  [#permalink]

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16 Nov 2016, 06:30
L BDC =95 deg.
In triangle ACD, L ACD = 180-(45+85) = 50 deg.
Since CD is bisector, L BCD = 50 deg.
In triangle BCD, L CBD = 180-(95+50) = 35 deg.=L ABC
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Re: If CD is a bisector in triangle ABC, what is ∠ABC?  [#permalink]

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16 Nov 2016, 06:58
Bunuel wrote:

If CD is a bisector in triangle ABC, what is ∠ABC?

A. 25°
B. 30°
C. 35°
D. 40°
E. 45°

Attachment:
T89000.png

angle ACD= angle DCB (angular bisector)
In triangle ADC, angle CDA+ angle CAD+ angle ACD= 180==> angle ACD= 50 = angle DCB
In Triangle CDB, angle CDB+ angle DCB+ angle CBD= 180==> angle CBD= 35 = Angle ABC
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Re: If CD is a bisector in triangle ABC, what is ∠ABC?  [#permalink]

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16 Nov 2016, 08:15
1
Bunuel wrote:

If CD is a bisector in triangle ABC, what is ∠ABC?

A. 25°
B. 30°
C. 35°
D. 40°
E. 45°

Attachment:
T89000.png

∠ CDA = 180° - 95° = 85°

Again, ∠ CDA = 180° - 85° - 45° = 50°

So , ∠ ACB = 100°

Hence, ∠ ACB = 180° - 45° - 100° = 35°

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Re: If CD is a bisector in triangle ABC, what is ∠ABC?  [#permalink]

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16 Nov 2016, 17:45
BDC + CDA = 180 ( As AB is a straight line)
95 + CDA = 180
Thus, CDA = 85.
This in triangle ADC, ACD = 180 - (45 + 85) = 50

As CD is the bisector, ACD = BCD = 50.
Thus in triangle BDC, cba = 180 - (95 + 50) = 35.

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Re: If CD is a bisector in triangle ABC, what is ∠ABC?  [#permalink]

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28 Feb 2017, 20:27
Bunuel wrote:

If CD is a bisector in triangle ABC, what is ∠ABC?

A. 25°
B. 30°
C. 35°
D. 40°
E. 45°

Attachment:
T89000.png

Hi Bunuel,

For DS purposes, if the question statement mentions that a line is bisector of the triangle, does it imply its just an angle bisector or both angle and bisector of the opposite side ?

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Joined: 02 Sep 2009
Posts: 58434
Re: If CD is a bisector in triangle ABC, what is ∠ABC?  [#permalink]

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03 Mar 2017, 02:01
1
Shruti0805 wrote:
Bunuel wrote:

If CD is a bisector in triangle ABC, what is ∠ABC?

A. 25°
B. 30°
C. 35°
D. 40°
E. 45°

Attachment:
T89000.png

Hi Bunuel,

For DS purposes, if the question statement mentions that a line is bisector of the triangle, does it imply its just an angle bisector or both angle and bisector of the opposite side ?

It's an angle bisector but on the GMAT it would have been written better saying that CD is a bisector of angle ACB.

A line from a vertex to the midpoint of the opposite side is called median.
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Re: If CD is a bisector in triangle ABC, what is ∠ABC?  [#permalink]

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23 Nov 2018, 09:16
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Re: If CD is a bisector in triangle ABC, what is ∠ABC?   [#permalink] 23 Nov 2018, 09:16
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