For isosceles triangle LMN, what is the measure of angle N?

Question

In isosceles triangle LMN, what is the measure of angle N?

(1) Side LN measures 4 inches
(2) Side MN measures  4*\sqrt 2  inches

Kudos for a correct  solution .

goldfinchmonster · Answer

Answer E.

Neither of the statements give information about the dimentions of two equal sides. In case if two equal sides are 4 in length, the angle measures would be different from the angle measures if the the two equal sides are 4 \sqrt{2}.

peachfuzz · Answer

In isosceles triangle LMN, what is the measure of angle N?

(1) Side LN measures 4 inches
Insufficient info
(2) Side MN measures  4*\sqrt 2  inches
Insufficient info

Combined we dont know if the LM side is one of the 2 options given in the statement. Insufficient

Answer:E

alphaseeker · Answer

Hi Bunuel,

I am a non native speaker. In my language it is usually given what sides are equal, or 
if the question says that LMN isosceles triangle, we can conclude that LM=MN.

I am not sure what the standard is in GMAT. In that question which sides are equal, LM=MN ??? How would we interpret the sides if no shapes are given?

Thank you

fontana · Answer

Answer C.

You know that LN=4 and MN=4 sqrt(2). As the triangle is isosceles, LM must be equal to 4. You can apply the law of cosines to find out the angles, when you know the sides of the triangle (if you really needed to calculate it). 
Even without knowing the law of cosines, the relationship 1:1:sqrt(2) must ring a bell, this is a right triangle, and the angle N must be equal to 45 deg.

ritigl · Answer

1. Insufficient 
2. Insufficient 
 
1+2 Sufficient 
The LMN triangle formed is right angled isosceles triangle right angled at L. This is so because the 45-45-90 triangle has values as 1-1- \sqrt{2} . This is pretty clear from the information about the two sides given as LN=4 and MN=4 \sqrt{2} . So MN is the hypotenuse and sides ML=LN.

Answer C.

kunal555 · Answer

Statement 1:-
It doesn't specify which 2 sides are equal.
INSUFFICIENT

Statement 2:- 
Again doesn't specify which 2 sides are equal.
INSUFFICIENT

On combining statement 1 and 2 , we get no new information. 
INSUFFICIENT

Answer:- E

rajarams · Answer

Consider 1) : Nothing can be conclusively said. We do not even know if it's the equal or the unequal side. Insufficient
2) Again, we know only one side. Nothing can be said about it.

1 and 2 put together:

We know two sides and the shorter one must be the equal side. So, the three sides are 4, 4, 4 \sqrt{2} . This is of the form 1 : 1 :  \sqrt{2}  ie., a 45-45-90 triangle. So,  \angle L = 90 (since it's the angle opposite to the larger side). The other angles must be 45 each, making  \angle N 45.

goldfinchmonster · Answer

Hi Raja,

"  two sides and the shorter one must be the equal side. So, the three sides are 4, 4, 4 \sqrt{2}   "

Can you tell why is this so. Why can't the equal sides be 4\sqrt{2}.

Vijay.

AbdurRakib · Answer

Statement (1) and (2) individually insufficient for providing inadequate information about isosceles to measure angle of N

By combining two statements we can find two sets of side for isosceles : (4 \sqrt{2} ,4 \sqrt{2} ,4) and (4,4,4 \sqrt{2} )

So the  Correct Answer is E

Shree9975 · Answer

Hi  Bunuel :

Why is the answer not C??
One side 4 and other 4sqrt2, and the triangle given is iscosceles, is it not enough for the triangle to be 45-45-90 triangle??

Thanks

joylive · Answer

Details of which sides are equal are not mentioned, also it is not possible to figure out from the statements which 2 sides are equal.

St. I --> LN = 4, what about other sides, which sides are similar, not useful
St. II --> MN =  4*\sqrt 2 , the angles can be 90-45-45 or 30-60-90, not useful.

Combined, both I n II does not help identify which sides are equal and also what are the angles.

Can't conclude anything, E is the answer

Nevernevergiveup · Answer

For isosceles triangle LMN, what is the measure of angle N?
(1) The lengths of all three sides of triangle LMN are the same.
(2) Angle L measures 60 degrees.

Kurtosis · Answer

St1: Indicates that the triangle is equilateral. So N should be equal to 60 --> Sufficient

St2: Suppose L is not isosceles and other two angles (M and N) are isosceles then angle of M or N = (180 - 60)/2 = 60. Indicates its an equilateral triangle.
Suppose L is isosceles with one more angle (say M) then the remaining angle must be 180 - 120 = 60. Again its an equilateral triangle. 
So St2 is sufficient.

Answer: D

winionhi · Answer

How were you able to deduce that the triangle is Equilateral from Statement 1?

Kurtosis · Answer

Hi,

The question I have answered is quite different from the merged topic.

I think there is some confusion with the answer choice in the main question. I have updated the OA in the main question to E.

dcummins · Answer

Official Explanation :
 
E. Beware the trap in this problem, which is designed to get you to think that triangle LMN must be an isosceles right triangle, in which case side LN would have to be 4. Because, however, the triangle isn't defined as a right triangle, side LN could also match side MN and be 4*sqrt 2. Because there are two different perimeters possible given the parameters of the question, the correct answer is E.

Basshead · Answer

An isosceles triangle has 2 even sides, which means 2 equal angles.

Each statement alone is clearly insufficient.

Combined, we know one side is 4 inches and another is  4*\sqrt 2  inches. However, we don't know which side is repeated. We could have two 4 inch sides or 2  4*\sqrt 2  inch sides. INSUFFICIENT.

Answer is E.

For isosceles triangle LMN, what is the measure of angle N?

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