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by eaakbari » Thu Nov 15, 2012 7:15 am
In the figure, point D divides side BC of triangle ABC into segments BD and DC of lengths 1 and 2 units respectively. Given that �ADC = 60º and �ABD = 45º, what is the measure of angle x in degrees? (Note:
Figure is not drawn to scale.)

A. 55
B. 60
C. 70
D. 75
E. 90
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by GMATGuruNY » Thu Nov 15, 2012 12:19 pm
atulmangal wrote:In the figure, point D divides side BC of triangle ABC into segments BD and DC of lengths 1 and 2 units respectively. Given that angle ADC = 60º and angle ABD = 45º, what is the measure of angle x in degrees? (Note: Figure is not drawn to scale.)

Image

(A) 55 (B) 60 (C) 70 (D) 75 (E) 90
Image
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by eaakbari » Fri Nov 16, 2012 7:52 am
Mitch,

How did you conclude DE = BD = 1

All we did prior to that was drop a perpendicular.
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by GMATGuruNY » Fri Nov 16, 2012 11:26 am
eaakbari wrote:Mitch,

How did you conclude DE = BD = 1

All we did prior to that was drop a perpendicular.
When a problem indicates that an angle is 60 degrees, TRY TO DRAW A 30-60-90 triangle.

It is given that CD=2 and that ∠CDA= 60.
When CE is drawn perpendicular to AD, ∠CED=90, with the result that ∆CED is a 30-60-90 triangle.
In a 30-60-90 triangle, the sides are proportioned x : x√3 : 2x.
Since CD=2, the sides of ∆CED are DE=1, CE=√3, and CD=2.
It is given in the problem that BD=1.
Thus:
DE=BD=1.
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