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

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

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New post 16 Nov 2016, 03:50
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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
T89000.png [ 7.37 KiB | Viewed 1980 times ]

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

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New post 16 Nov 2016, 05:30
L BDC =95 deg.
L ADC=180-95 = 85 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
Hence answer C.
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Re: If CD is a bisector in triangle ABC, what is ∠ABC?  [#permalink]

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New post 16 Nov 2016, 05:58
Bunuel wrote:
Image
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
C
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Re: If CD is a bisector in triangle ABC, what is ∠ABC?  [#permalink]

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New post 16 Nov 2016, 07:15
1
Bunuel wrote:
Image
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°

Answer will be (C) 35°
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Re: If CD is a bisector in triangle ABC, what is ∠ABC?  [#permalink]

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New post 16 Nov 2016, 16:45
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.

Answer = (c)
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Re: If CD is a bisector in triangle ABC, what is ∠ABC?  [#permalink]

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New post 28 Feb 2017, 19:27
Bunuel wrote:
Image
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 ?

Thanks in advance. :)
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Joined: 02 Sep 2009
Posts: 51227
Re: If CD is a bisector in triangle ABC, what is ∠ABC?  [#permalink]

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New post 03 Mar 2017, 01:01
1
Shruti0805 wrote:
Bunuel wrote:
Image
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 ?

Thanks in advance. :)


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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New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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

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