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by sukhman » Sun Oct 06, 2013 12:40 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 Angle ADC =60 and Angle ABD =45 , what is the measure of angle x in degrees ?

55 60 70 75 90
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by GMATGuruNY » Sun Oct 06, 2013 3:27 am
Image

In the figure above, 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
One angle = 60.
Another angle = 45.
Look for 30-60-90 and 45-45-90 triangles.
Click on the figures below to enlarge them.

Step 1:
Image
Draw 30-60-90 ∆CDE.
Result:
DE=BD=1.

Step 2:
Image
Since DE=BD, draw ISOSCELES ∆BDE.
Add to the figure the implied angle measurements, as shown above.

Step 3:
Image
Notice that ∆BCE and ∆ABE are also ISOSCELES.

Step 4:
Image
Since BC=CE=AE, ∆ACE also is ISOSCELES.
Add to the figure the implied angle measurements, as shown above.
Result:
∠ACD = 45+30 = 75.

The correct answer is D.
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by Premalatha Anand » Fri Oct 18, 2013 5:03 pm
Ha ! too complicated! anybody easier way to und. pls help!
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by Uva@90 » Fri Oct 18, 2013 6:06 pm
Premalatha Anand wrote:Ha ! too complicated! anybody easier way to und. pls help!
Hi Premalatha Anand,
One more solution is provided in Manhattan Forum.(Pls check there)

Regards,
uva.
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