Geometry

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sukhman: Master | Next Rank: 500 Posts; Posts: 202; Joined: Sun Sep 08, 2013 11:51 amFollowed by: 2 members; Thanked: 3 times

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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Source: Beat The GMAT — Problem Solving | Sun Oct 06, 2013 12:40 am

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sun Oct 06, 2013 3:27 am

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:

Draw 30-60-90 âˆ†CDE.
Result:
DE=BD=1.

Step 2:

Since DE=BD, draw ISOSCELES âˆ†BDE.
Add to the figure the implied angle measurements, as shown above.

Step 3:

Notice that âˆ†BCE and âˆ†ABE are also ISOSCELES.

Step 4:

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

The correct answer is D.

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Premalatha Anand: Junior | Next Rank: 30 Posts; Posts: 10; Joined: Wed Sep 25, 2013 9:38 am

by Premalatha Anand » Fri Oct 18, 2013 5:03 pm

Ha ! too complicated! anybody easier way to und. pls help!

Regards
Premalatha

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Uva@90: Master | Next Rank: 500 Posts; Posts: 490; Joined: Thu Jul 04, 2013 7:30 amFollowed by: 5 members; Location: Chennai, India; Thanked: 83 times

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.

Known is a drop Unknown is an Ocean

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