Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 23 Feb 2010
Posts: 13

In isosceles triangle RST what is the measure of angle R?
[#permalink]
Show Tags
08 Mar 2010, 21:46
Question Stats:
76% (00:50) correct 24% (00:48) wrong based on 726 sessions
HideShow timer Statistics
In isosceles triangle RST what is the measure of angle R? (1) The measure of ∠T is 100°. (2) The measure of ∠S is 40°.
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 65187

Re: In isosceles triangle RST what is the measure of angle R?
[#permalink]
Show Tags
20 Mar 2012, 08:45
In isosceles triangle RST what is the measure of angle R?Triangle RST is isosceles means that two of its angles are equal. (1) The measure of angle T is 100 degrees > since no other angle can be equal to 100 degrees (because in this case the sum of the angles will be more than 180 degrees) then the other two angles, R and S, are equal: R=(180100)/2=40. Sufficient. (2) The measure of angle S is 40 degrees > consider two cases: S=R=40 and T=100 AND S=40 and R=T=70. Not sufficient. Answer: A.
_________________




SVP
Joined: 14 Apr 2009
Posts: 2272
Location: New York, NY

Re: In isosceles triangle RST what is the measure of angle R?
[#permalink]
Show Tags
09 Mar 2010, 10:00
gmatgg, This is a fairly one simple one that you should spend no more than 30 seconds on.
The keyword is "isosceles"which means 2 sides are the same and also...2 angles are the same
With statement (1), you are told measure of angle T is 100 degrees. You already know an entire triangle = 180 degrees.
So either one of the other angles also equals 100 degrees, or the other two angles not mentioned are equivalent.
Well, it's impossible for one of the other angles to also be 100 degrees, because that would exceed that total of 180 degrees possible in a triangle.
So the only choice that makes sense is to have the other two angles equal and everything adds to 180.
In other words, the other 2 angles combined must equal the difference between 180 and 100. Mathematically, 180  100 = 80 and then divide that by 2 to get 40 degrees.
So (1) by itself is good enough.
Statement (2) is just telling us that one angle is 40 degrees. Well, what possibilities are there? You could have one 40 degrees and then the other two angles are equivalent and all 3 add up to 180. OR you can have another angle that is also 40 degrees and the third angle would add up to 180. In other words, you'd have two possibilities:
1) 40  70  70 (adds up to 180) or 2) 40  40  100 (also adds up to 180)
Since you have MULTIPLE possibilities with statement (2), then you do not have enough information to definitively say what the answer is. So Statement (2) is not good enough. With (1) good and (2) no good, answer is (A).
Hope that helps.




Director
Joined: 14 Dec 2012
Posts: 670
Location: India
Concentration: General Management, Operations
GPA: 3.6

Re: In isosceles triangle RST what is the measure of angle R?
[#permalink]
Show Tags
12 Aug 2013, 02:31
enigma123 wrote: In isosceles triangle RST what is the measure of angle R? (1) The measure of angle T is 100 degrees. (2) The measure of angle S is 40 degrees. How come statemen1 is correct and not C?
Is it because of if one angle is 100 then others have to be 40 and 40 as the triangle is isoceles.
But then if that's the case why statement 2 is not sufficient? IN ISOCELES TRIANGLE ANGLES ARE ALWAYS. X,X,(1802X) (1) The measure of angle T is 100 degrees.CLEARLY X CANT BE equal to 100 because in that case sum of angle will exceed 180 degrees therefore 1802X = 100. CLEARLY X=40 SUFFICIENT. (2) The measure of angle S is 40 degrees.IF X CAN BE 40 OR 1802X CAN BE 40 WE ARE GETTING 2 DIFFERENT VALUES OF X. HENCE INSUFFICIENT. HENCE A
_________________
When you want to succeed as bad as you want to breathe ...then you will be successfull....
GIVE VALUE TO OFFICIAL QUESTIONS...
GMAT RCs VOCABULARY LIST: http://gmatclub.com/forum/vocabularylistforgmatreadingcomprehension155228.html learn AWA writing techniques while watching video : http://www.gmatprepnow.com/module/gmatanalyticalwritingassessment : http://www.youtube.com/watch?v=APt9ITygGss



Intern
Joined: 18 Aug 2013
Posts: 7

Re: In isosceles triangle RST what is the measure of angle R?
[#permalink]
Show Tags
23 Jun 2014, 03:04
HI, Thanks a lot for the reply! That is very useful. So I suppose for 2, we cannot assume that S is the adjacent angle to two isosceles angles? As this is what I did and I thought that it was sufficient. Thanks a lot again, Really appreciate it! Bunuel wrote: In isosceles triangle RST what is the measure of angle R?
Triangle RST is isosceles means that two of its angles are equal.
(1) The measure of angle T is 100 degrees > since no other angle can be equal to 100 degrees (because in this case the sum of the angles will be more than 180 degrees) then the other two angles, R and S, are equal: R=(180100)/2=40. Sufficient.
(2) The measure of angle S is 40 degrees > consider two cases: S=R=40 and T=100 AND S=40 and R=T=70. Not sufficient.
Answer: A.



Math Expert
Joined: 02 Sep 2009
Posts: 65187

Re: In isosceles triangle RST what is the measure of angle R?
[#permalink]
Show Tags
23 Jun 2014, 03:19
Yela wrote: HI, Thanks a lot for the reply! That is very useful. So I suppose for 2, we cannot assume that S is the adjacent angle to two isosceles angles? As this is what I did and I thought that it was sufficient. Thanks a lot again, Really appreciate it! Bunuel wrote: In isosceles triangle RST what is the measure of angle R?
Triangle RST is isosceles means that two of its angles are equal.
(1) The measure of angle T is 100 degrees > since no other angle can be equal to 100 degrees (because in this case the sum of the angles will be more than 180 degrees) then the other two angles, R and S, are equal: R=(180100)/2=40. Sufficient.
(2) The measure of angle S is 40 degrees > consider two cases: S=R=40 and T=100 AND S=40 and R=T=70. Not sufficient.
Answer: A. Yes, from (2) we cannot assume that S is one of the two angles that are equal.
_________________



Intern
Joined: 04 Jun 2014
Posts: 44

Re: In isosceles triangle RST what is the measure of angle R?
[#permalink]
Show Tags
30 Aug 2014, 04:54
I have a general question: The order of the letters after the sign of the triangle, here <RST, does not give any indication of the order of the angles? Sorry I don't know how to insert the proper angle sign.



Math Expert
Joined: 02 Sep 2009
Posts: 65187

Re: In isosceles triangle RST what is the measure of angle R?
[#permalink]
Show Tags
01 Sep 2014, 06:03
lou34 wrote: I have a general question: The order of the letters after the sign of the triangle, here <RST, does not give any indication of the order of the angles? Sorry I don't know how to insert the proper angle sign. Order of letters for a triangle does not matter. Triangles RST, RTS, STR, ... are all the same. As for other polygons (quadrilaterals, pentagons, ...): here order of the letters is important meaning that rectangle ABCD (diagonals here are AC and BD) is different from rectangle ACBD (diagonals here are AB and CD). Usually OG uses sequential (ABCDE...) labeling. Also, most of the times the labeling is clockwise but I wouldn't worry about it because if a diagram is not given then this won't be important (meaning that you can consider it clockwise as well as counterclockwise).
_________________



Manager
Joined: 27 Aug 2014
Posts: 63

Re: In isosceles triangle RST what is the measure of angle R?
[#permalink]
Show Tags
20 Nov 2014, 05:14
Bunuel wrote: In isosceles triangle RST what is the measure of angle R?
Triangle RST is isosceles means that two of its angles are equal.
(1) The measure of angle T is 100 degrees > since no other angle can be equal to 100 degrees (because in this case the sum of the angles will be more than 180 degrees) then the other two angles, R and S, are equal: R=(180100)/2=40. Sufficient.
(2) The measure of angle S is 40 degrees > consider two cases: S=R=40 and T=100 AND S=40 and R=T=70. Not sufficient.
Answer: A. Hi Bunuel How can S=R=40 because that would take it out of the triangle definition isnt it? Sum of two smaller sides wont be greater than the longest side so can it be a valid scenario? Does this rule only apply to sides measure and not angles in a triangle?



Math Expert
Joined: 02 Sep 2009
Posts: 65187

Re: In isosceles triangle RST what is the measure of angle R?
[#permalink]
Show Tags
20 Nov 2014, 07:06
sinhap07 wrote: Bunuel wrote: In isosceles triangle RST what is the measure of angle R?
Triangle RST is isosceles means that two of its angles are equal.
(1) The measure of angle T is 100 degrees > since no other angle can be equal to 100 degrees (because in this case the sum of the angles will be more than 180 degrees) then the other two angles, R and S, are equal: R=(180100)/2=40. Sufficient.
(2) The measure of angle S is 40 degrees > consider two cases: S=R=40 and T=100 AND S=40 and R=T=70. Not sufficient.
Answer: A. Hi Bunuel How can S=R=40 because that would take it out of the triangle definition isnt it? Sum of two smaller sides wont be greater than the longest side so can it be a valid scenario? Does this rule only apply to sides measure and not angles in a triangle? Yes, the rule is about the lengths of the sides. The length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.For the angles of a triangle we have that their sum must be 180 degrees. Check for more here: mathtriangles87197.htmlHope it helps.
_________________



GMAT Club Legend
Joined: 11 Sep 2015
Posts: 4959
Location: Canada

Re: In isosceles triangle RST what is the measure of angle R?
[#permalink]
Show Tags
19 Apr 2018, 14:09
gmatgg wrote: In isosceles triangle RST what is the measure of angle R?
(1) The measure of angle T is 100 degrees.
(2) The measure of angle S is 40 degrees.
IMPORTANT: In an isosceles triangle there are 2 IDENTICAL angles, and 1 LONE angle. Target question: What is measure of ∠R? Statement 1: ∠T = 100 degrees We should recognize that ∠T CANNOT be one of the identical angles. If this were the case, we'd have two angles with measures of 100 degrees each, which would result in a triangle in which the sum of the angles is GREATER than 180 degree (which is IMPOSSIBLE) So, we can conclude that ∠T must be the LONE angle, which means ∠R and ∠S are the two IDENTICAL angles. Since the sum of the 3 angles must be 180, we can conclude that ∠R = 40, ∠S = 40, and ∠T = 100 Since we can answer the target question with certainty, statement 1 is SUFFICIENT Statement 2: ∠S = 40 degrees Here are two possible cases to consider: Case a: ∠S is the LONE angle, in which case the ∠R = 70, ∠S = 40, and ∠T = 70 Case b: ∠S is one of the IDENTICAL angles, in which case we could have ∠R = 40, ∠S = 40, and ∠T = 100 Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT Answer = A Cheers, Brent
_________________
Test confidently with gmatprepnow.com



Manager
Joined: 09 Jun 2018
Posts: 184
Location: United States
GPA: 4
WE: Operations (Manufacturing)

Re: In isosceles triangle RST what is the measure of angle R?
[#permalink]
Show Tags
31 Oct 2018, 10:28
Stmt 1: R is 100 deg, so remaining two angles have a sum of 80 deg. Since it is an isosceles triangle, 2 angles are equal. Now, another angle cannot be equal to R as sum of just two angles will be more than 180 deg. Hence, the other two angles have to be half of 80 each, or 40 deg. Hence suff. Eliminate B,C,E
Stmt 2: T is 40 deg, so remaining two angles have a sum of 140 deg. If one of the other two angles is 40, then third is 100, but it can be possible than the other two are equal to 70 deg each as well. Hence insuff. Eliminate D.
Hence Option A



Manager
Joined: 08 Sep 2008
Posts: 122
Location: India
Concentration: Operations, General Management
GPA: 3.8
WE: Operations (Transportation)

Re: In isosceles triangle RST what is the measure of angle R?
[#permalink]
Show Tags
31 Oct 2018, 10:28
isosceles ∆ RST, what is the measure of ∠ S? St:1 ∠ R is 100 ◦ R+S+T=180 R=100 so S+T has to 80 Isosceles so S=T=40 Sufficient. St:2 The measure of ∠ T is 40 ◦ . S+R=140 So s=r=70 ( if side correspond to angle s and r are equal) But, If Sides correspond to angle T and angle S is equal then s=40
Two values \ Not sufficient.
Answer: A



Manager
Joined: 07 May 2016
Posts: 55

Re: In isosceles triangle RST what is the measure of angle R?
[#permalink]
Show Tags
07 Jun 2019, 01:23
gmatgg wrote: In isosceles triangle RST what is the measure of angle R?
(1) The measure of ∠T is 100°.
(2) The measure of ∠S is 40°. I read the options as angle T is less than 100 degreee!! All my analysis of this question is wrong



NonHuman User
Joined: 09 Sep 2013
Posts: 15408

Re: In isosceles triangle RST what is the measure of angle R?
[#permalink]
Show Tags
30 Jun 2020, 21:48
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________




Re: In isosceles triangle RST what is the measure of angle R?
[#permalink]
30 Jun 2020, 21:48




