gmat preparation courses

It is currently Tue Apr 24, 2018 8:27 am

All times are UTC - 5 hours [ DST ]




Post new topic Reply to topic  [ 2 posts ] 
Author Message
 Post subject: GMAT Geometry
PostPosted: Thu Mar 01, 2012 7:43 am 
Offline

Joined: Sun May 30, 2010 3:15 am
Posts: 424
Image
In triangle ABC, DB and DC are angle bisectors and the angle BAC = 60°. If angle DCB is 40°, what is the degree measure of angle BDC? (Note: Figure not drawn to scale.)

A. 130°
B. 120°
C. 100°
D. 80°
E. 75°

(B) First of all remember that the sum of all angles in a triangle is equal to 180°. We are told that angle BAC = 60°. That leaves 120° to be split between angles ABC and ACB. We know that DC and DB are angle bisectors (an angle bisector can be described as a line segment that divides an angle into two equal angles), so the sum of angles DBC and DCB is 120°/2 = 60°. BDC is the third angle in triangle BDC. Therefore it equals 180° – 60° = 120°. The correct answer is B.
----------
I do not understand why the answer is 120° and not 100°. If as you say, DB and DC are angle bisectors and DCB is 40° degrees (as stated in the question) CBD should also be 40° (which lets CBA and ACB as 60 degrees angles). If all the angles must be 180 degrees 180° – 80° = 100°.


Attachments:
triangles.gif [3.19 KiB]
Not downloaded yet
Top
 Profile  
 
 Post subject: Re: GMAT Geometry
PostPosted: Thu Mar 01, 2012 7:58 am 
Offline

Joined: Sun May 30, 2010 2:23 am
Posts: 498
Quote:
CBD should also be 40° (which lets CBA and ACB as 60 degrees angles).
Angles CBA and ACB are NOT 60° angles.
An angle bisector divides that angle into two equal angles. So if angle DCB is 40° then angle ACB is 80°. You can calculate angle CBA, it equals 180° – 60° – 80° = 40°.
So angle CBD is NOT 40°. It equals 40°/2 = 20°.


Top
 Profile  
 
Display posts from previous:  Sort by  
Post new topic Reply to topic  [ 2 posts ] 

All times are UTC - 5 hours [ DST ]


Who is online

Users browsing this forum: No registered users and 2 guests


You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot post attachments in this forum

Search for:
Jump to:  
cron
Powered by phpBB © 2000, 2002, 2005, 2007 phpBB Group