Author 
Message 
TAGS:

Hide Tags

SVP
Joined: 08 Jul 2010
Posts: 2334
Location: India
GMAT: INSIGHT
WE: Education (Education)

Re: In the figure, point D divides side BC of triangle ABC into segments
[#permalink]
Show Tags
12 Nov 2016, 20:57
enigma123 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 ÐADC = 60º and ÐABD = 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 Any idea guys what will be the correct answer please? Also any idea how can I cut and paste the pictures in my post? Is it possible? Attachment: The attachment Triangle.png is no longer available Answer: Option D Please check solution
Attachments
File comment: www.GMATinsight.com
12.jpg [ 110.35 KiB  Viewed 1706 times ]
_________________
Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha email: info@GMATinsight.com I Call us : +919999687183 / 9891333772 Online OneonOne Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html
22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION



Manager
Joined: 20 Apr 2014
Posts: 95

Re: In the figure, point D divides side BC of triangle ABC into segments
[#permalink]
Show Tags
15 Nov 2016, 22:36
Hi Bunuel please clarify how we decide that triangle CAO is isoseles and AO and line AO is s.root of 3 Also how we decide that line OB is s.root of 3 thanks in advance



Intern
Joined: 09 Nov 2015
Posts: 30
GMAT 1: 640 Q49 V29 GMAT 2: 720 Q50 V38

Re: In the figure, point D divides side BC of triangle ABC into segments
[#permalink]
Show Tags
Updated on: 14 Feb 2017, 11:32
Bunuel wrote: enigma123 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 ÐADC = 60º and ÐABD = 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 Any idea guys what will be the correct answer please? Also any idea how can I cut and paste the pictures in my post? Is it possible? Complete solution for all the angles is in the image below: x=45+30=75. Notes: Sides with one blue segment crossing them are equal and sides with two blues segments crossing them are equal too. CO is perpendicular to AD > OD=1 (from 306090 right triangle property as sides are in ratio \(1:\sqrt{3}:2\)) > as OD=BD=1 then ODB is an isosceles triangle. <CDO and <BDO are supplementary to each other (supplementary angles are two angles that add up to 180°), so <BDO=120 > <DAB=180(120+45)=15. As ODB is an isosceles triangle > <DOB=<DBO=30. <OBA=4530=15 > AOB is an isosceles triangle, so OA=OB. Also COB is an isosceles triangle, so CO=OB > OA=CO=OB. So, AOC is an isosceles triangle > <CAO=<OCA=45 (as <COA=90) > x=45+30=75. Answer: D. P.S. You can attach image files directly to the post. Attachment: Triangle complete.PNG Hello sir, Can you explain me by what properties you arrived at the solution? By which property you drew CO such that it meets at the point where BO also meets to form such isosceles triangles?
Originally posted by ravi19012015 on 14 Feb 2017, 04:49.
Last edited by ravi19012015 on 14 Feb 2017, 11:32, edited 1 time in total.



Intern
Joined: 08 Mar 2016
Posts: 33

Re: In the figure, point D divides side BC of triangle ABC into segments
[#permalink]
Show Tags
14 Feb 2017, 11:04
Brunnel :
Could we have used a 45:45:90 for the triangle DOB by drawing DO perpendicular to AB. However, Doing this wont take us anywhere near the triangle ADC correct?
So. I guess my question is, Though I can understand by seeing values of sides and angles in triangles that I somehow have to use sides and angles combined to get my answer, and one of the most popular way of doing those in GMAT is using 45:45:90 or 30:60:90 triangles, but how do choose at one go which triangle should I use? What should be the thinking behind it? Which triangle to draw the perpendicular from among the trianlges ACD and ADB?



Intern
Joined: 26 Jun 2017
Posts: 1

Re: In the figure, point D divides side BC of triangle ABC into segments
[#permalink]
Show Tags
26 Jun 2017, 16:45
ODB is an isosceles triangle > <DOB=<DBO=30. <OBA=4530=15 > AOB is an isosceles triangle, so OA=OB. Also COB is an isosceles triangle, so CO=OB > OA=CO=OB. So, AOC is an isosceles triangle > <CAO=<OCA=45 (as <COA=90) > x=45+30=75.



Intern
Joined: 21 Jan 2017
Posts: 33

Re: In the figure, point D divides side BC of triangle ABC into segments
[#permalink]
Show Tags
09 Jul 2017, 17:04
navigator123 wrote: enigma123 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 ÐADC = 60º and ÐABD = 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
Any idea guys what will be the correct answer please? Also any idea how can I cut and paste the pictures in my post? Is it possible? Is it correct to tell that <CAD : <BAD = 2:1 because, CD:DB = 2:1? Even I have imagined in the same way and got 90 as the answer. I understood the explanation from the figures but my doubt is why can't <CAD = 30? when <DAB=15? If CD:DB=2:1, is it wrong to assume <CAD:<DAB is also 2:1??? please answer. Thanks, Uma



Current Student
Joined: 22 Sep 2016
Posts: 186
Location: India
GPA: 4

Re: In the figure, point D divides side BC of triangle ABC into segments
[#permalink]
Show Tags
11 Jul 2017, 00:51
What is the source of this question?
_________________
Desperately need 'KUDOS' !!



Senior CR Moderator
Status: Long way to go!
Joined: 10 Oct 2016
Posts: 1387
Location: Viet Nam

Re: In the figure, point D divides side BC of triangle ABC into segments
[#permalink]
Show Tags
11 Jul 2017, 00:57



Mannheim Thread Master
Status: It's now or never
Joined: 10 Feb 2017
Posts: 230
Location: India
GPA: 3
WE: Consulting (Consulting)

Re: In the figure, point D divides side BC of triangle ABC into segments
[#permalink]
Show Tags
21 Jul 2017, 00:54
Although I got the right answer, I wanted to understand simpler equation to derive the answer. Can someone help!
_________________
20172018 MBA Deadlines
Threadmaster for Bschool Discussions Class of 2019: Mannheim Business School Class 0f 2020: HHL Leipzig



Senior Manager
Joined: 29 Jun 2017
Posts: 487
GPA: 4
WE: Engineering (Transportation)

Re: In the figure, point D divides side BC of triangle ABC into segments
[#permalink]
Show Tags
17 Aug 2017, 09:30
Attachment:
IMG_6850.JPG [ 1.67 MiB  Viewed 1495 times ]
. see attached pic Answer is 75 degrees.
_________________
Give Kudos for correct answer and/or if you like the solution.



Intern
Joined: 28 Sep 2017
Posts: 2

Re: In the figure, point D divides side BC of triangle ABC into segments
[#permalink]
Show Tags
06 Dec 2017, 20:10
Hi bunuel,
Sorry for bumping. A quick question.
How do we know that AD is not equal to 1. If it is equal to 1 then the ratio 2:1 when a perpendicular is drawn does not hold good right? Am i missing something?



Math Expert
Joined: 02 Sep 2009
Posts: 49303

Re: In the figure, point D divides side BC of triangle ABC into segments
[#permalink]
Show Tags
06 Dec 2017, 20:40



Intern
Joined: 30 Sep 2017
Posts: 39
Location: India
Concentration: Entrepreneurship, General Management
GPA: 3.7
WE: Engineering (Energy and Utilities)

Re: In the figure, point D divides side BC of triangle ABC into segments
[#permalink]
Show Tags
07 Dec 2017, 09:43
Hi Bunuelis this a GMAT level question? seems too tough
_________________
If you like my post, motivate me by giving kudos...



Manager
Joined: 02 Jul 2016
Posts: 116

Re: In the figure, point D divides side BC of triangle ABC into segments
[#permalink]
Show Tags
14 Apr 2018, 11:57
Bunuel wrote: enigma123 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 ÐADC = 60º and ÐABD = 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 Any idea guys what will be the correct answer please? Also any idea how can I cut and paste the pictures in my post? Is it possible? Complete solution for all the angles is in the image below: x=45+30=75. Notes: Sides with one blue segment crossing them are equal and sides with two blues segments crossing them are equal too. CO is perpendicular to AD > OD=1 (from 306090 right triangle property as sides are in ratio \(1:\sqrt{3}:2\)) > as OD=BD=1 then ODB is an isosceles triangle. <CDO and <BDO are supplementary to each other (supplementary angles are two angles that add up to 180°), so <BDO=120 > <DAB=180(120+45)=15. As ODB is an isosceles triangle > <DOB=<DBO=30. <OBA=4530=15 > AOB is an isosceles triangle, so OA=OB. Also COB is an isosceles triangle, so CO=OB > OA=CO=OB. So, AOC is an isosceles triangle > <CAO=<OCA=45 (as <COA=90) > x=45+30=75. Answer: D. P.S. You can attach image files directly to the post. Attachment: Triangle complete.PNG Great Explanation!! I didn't undertsand how is Triangle COB Isosceles??



Intern
Joined: 15 Apr 2018
Posts: 3

Re: In the figure, point D divides side BC of triangle ABC into segments
[#permalink]
Show Tags
15 Apr 2018, 10:19
vigrah wrote: say angle CAB=y since sum of angles in a triangle is 180 x+y+45=180 x+y=135 equation 1
line AD is dividing BC in 2:1 ratio hence X+2/3Y+60=180[u](can you explain this step please?
X+2/3y=120 equation 2 solving equation 1 &2 we get x=75 answer is D



Intern
Joined: 30 Sep 2017
Posts: 39
Location: India
Concentration: Entrepreneurship, General Management
GPA: 3.7
WE: Engineering (Energy and Utilities)

Re: In the figure, point D divides side BC of triangle ABC into segments
[#permalink]
Show Tags
15 Apr 2018, 16:54
Hii Is this GMAT level Question? I am finding it tough to solve under time pressure in 2 minutes.
_________________
If you like my post, motivate me by giving kudos...



CEO
Joined: 12 Sep 2015
Posts: 2878
Location: Canada

Re: In the figure, point D divides side BC of triangle ABC into segments
[#permalink]
Show Tags
17 Apr 2018, 06:44
enigma123 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 ÐADC = 60º and ÐABD = 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 Attachment: Triangle.png Attachment: task%236.png First let's add a line from point C so that it is PERPENDICULAR to line AD Also, note that, ∠EDB is 120° since it lies on a line with a 60° angle. Since we already know 2 angles in ∆CED, we can see that the remaining angle, ∠ECD, is 30°, which means ∆CED is a 306090 right triangle. So, ∆CED is a 306090 right triangle AND we know that the hypotenuse CD has length 2, we can conclude that side ED has length 1. Now draw a line from E to B. Since ED = EB (both have length 1), we can see that ∆EDB is an ISOSCELES TRIANGLE, which means the two remaining angles are each 30° Next, ∠EAB is 150° since it shares a line with a 30° angle Also, since we were originally told that ∠CBA is 45°, we can conclude that ∠ABE is 15° Now focus on ∆CBE Notice that this triangle is an ISOSCELES triangle, because ∠ECB = ∠EBC = 30° This means that side EC = side EB Now focus on ∆EAB Since we already know two of the angles in this triangle (150° and 15°), we can conclude that = ∠EAB = 15° Stay focused on ∆EAB This triangle is an ISOSCELES triangle, because ∠EAB = ∠EBA = 15° This means that side AE = side EB Now focus on ∆ACE Since CE = EA, this is an ISOSCELES triangle Since one angle = 90°, the other two angles are each 45° At this point, we can see that x = 45° + 30° = 75° Answer: D Cheers, Brent
_________________
Brent Hanneson – GMATPrepNow.com
Sign up for our free Question of the Day emails



Intern
Joined: 18 May 2016
Posts: 27

Re: In the figure, point D divides side BC of triangle ABC into segments
[#permalink]
Show Tags
29 May 2018, 02:49
vigrah wrote: say angle CAB=y since sum of angles in a triangle is 180 x+y+45=180 x+y=135 equation 1
line AD is dividing BC in 2:1 ratio hence X+2/3Y+60=180 X+2/3y=120 equation 2 solving equation 1 &2 we get x=75 answer is D This answer is wrong. Solving this system does not yield x=75, but x=90, and y=45. This answer should not have so many kudos, it is very misleading.



Manager
Joined: 07 Jun 2018
Posts: 110

Re: In the figure, point D divides side BC of triangle ABC into segments
[#permalink]
Show Tags
20 Jun 2018, 09:20
danzig wrote: Bunuel,
How can we know that we had to draw a perpendicular line from vertex C? , Why not from vertex D?, for example?
Thanks! Someone should please address this question. Thanks! Posted from my mobile device



Intern
Joined: 04 Oct 2017
Posts: 49

Re: In the figure, point D divides side BC of triangle ABC into segments
[#permalink]
Show Tags
31 Jul 2018, 07:54
vigrah wrote: say angle CAB=y since sum of angles in a triangle is 180 x+y+45=180 x+y=135 equation 1
line AD is dividing BC in 2:1 ratio hence X+2/3Y+60=180 X+2/3y=120 equation 2 solving equation 1 &2 we get x=75 answer is D Hi, Can you please explain how you arrived at X + 2/3Y +60 = 180????




Re: In the figure, point D divides side BC of triangle ABC into segments &nbs
[#permalink]
31 Jul 2018, 07:54



Go to page
Previous
1 2 3
[ 60 posts ]



