Measure of angle x

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Measure of angle x

by beat_gmat_09 » Tue Nov 09, 2010 1:14 am
In the figure to the right, point D divides side BC of triangle ABC into segments BD and DC of lengths 1 and 2 units respectively. Given that Angle ADC = 60 and Angle ABD = 45, what is the measure of angle x? (Note: Figure is not drawn to scale.)

(A) 55
(B) 60
(C) 70
(D) 75
(E) 90

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by goyalsau » Tue Nov 09, 2010 3:45 am
I think it should be E,

Angle ADC is the exterior angle of Traingle ADC,

Angle BAD is 15,

as the segment AD divides the line CB in the ratio of 1:2,

Angle BAD, must be half of Angle CAD,

by this relation, Angle DAC is 30 ,

we have two angles of a triangle so angle C must be 90,
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by beat_gmat_09 » Tue Nov 09, 2010 4:07 am
goyalsau wrote:I think it should be E,

Angle ADC is the exterior angle of Traingle ADC,

Angle BAD is 15,

as the segment AD divides the line CB in the ratio of 1:2,

Angle BAD, must be half of Angle CAD,

by this relation, Angle DAC is 30 ,

we have two angles of a triangle so angle C must be 90,
E is incorrect.
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by goyalsau » Tue Nov 09, 2010 5:23 am
beat_gmat_09 wrote:
goyalsau wrote:I think it should be E,

Angle ADC is the exterior angle of Traingle ADC,

Angle BAD is 15,

as the segment AD divides the line CB in the ratio of 1:2,

Angle BAD, must be half of Angle CAD,

by this relation, Angle DAC is 30 ,

we have two angles of a triangle so angle C must be 90,
E is incorrect.
What is the OA,
Do you have the explanation...
IF you have please post it then,
Saurabh Goyal
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by beat_gmat_09 » Tue Nov 09, 2010 7:02 am
goyalsau wrote:
beat_gmat_09 wrote:
goyalsau wrote:I think it should be E,

Angle ADC is the exterior angle of Traingle ADC,

Angle BAD is 15,

as the segment AD divides the line CB in the ratio of 1:2,

Angle BAD, must be half of Angle CAD,

by this relation, Angle DAC is 30 ,

we have two angles of a triangle so angle C must be 90,
E is incorrect.
What is the OA,
Do you have the explanation...
IF you have please post it then,
OA is D. I dont have explanation.
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by GMATGuruNY » Tue Nov 09, 2010 10:07 am
beat_gmat_09 wrote:In the figure to the right, point D divides side BC of triangle ABC into segments BD and DC of lengths 1 and 2 units respectively. Given that Angle ADC = 60 and Angle ABD = 45, what is the measure of angle x? (Note: Figure is not drawn to scale.)

(A) 55
(B) 60
(C) 70
(D) 75
(E) 90

Image
This is a very hard problem to solve without using trigonometry. The trick is to draw a 30:60:90 triangle and notice all the isosceles triangles that are created.

For one possible solution, please see the attachment.
Attachments
BTG_angle_x.pdf
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