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In isosceles triangle RST what is the measure of angle R?

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rmyoungsc
 Post subject: In isosceles triangle RST what is the measure of angle R?
 Post Posted: Thu Aug 20, 2009 5:11 pm 
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Course Students


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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.

Statement 1 is sufficient because the other 2 angles must be 40 degrees.

Statement 2 seems to me to be sufficient as well. Because the sum of any 2 angles in a triangle must be greater than the 3rd angle, and since S is 40 degrees, wouldn't the other 2 angles have to be equal to 70 degrees?

The answer is A apparently.
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furtadovinod
 Post subject: Re: In isosceles triangle RST what is the measure of angle R?
 Post Posted: Thu Aug 20, 2009 10:13 pm 
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rmyoungsc 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.

Statement 1 is sufficient because the other 2 angles must be 40 degrees.

Statement 2 seems to me to be sufficient as well. Because the sum of any 2 angles in a triangle must be greater than the 3rd angle, and since S is 40 degrees, wouldn't the other 2 angles have to be equal to 70 degrees?

The answer is A apparently.


That is not correct. Did you read it from somewhere? The only rule I know that applies to all triangles is that the sum of all the 3 angles of a triangle must be equal to 180 degrees.

Use your logic on the first statement. The angles are 100 degrees, 40 degrees and 40 degrees. The sum of the angles with measure 40 degrees is NOT greater than the measure of the angle with 100 degrees.
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himadribora
 Post subject: Re: In isosceles triangle RST what is the measure of angle R?
 Post Posted: Fri Aug 21, 2009 2:42 pm 
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I think it goes like this:

First Statement: If T is 100 degrees, it cannot be one of the equal angles of the isoceles triangle...because 100 + 100 = 200 > 180, even before taking into account the third angle. So the remaining two angles have to be the equal ones i.e. 180 - 100 = 80 / 2 = 40 = R = S. SUFFICIENT

Second Statement: S=40. From this we cannot be sure if S is one of the equal angles. If S is NOT one of the equal angles, then S=40 and R=T=70 (180-40 = 140/2). If S was one of the equal angles then, S=40 = R or T i.e. If R = 40, then T = 110 OR if T = 40, then R = 110. INSUFFICIENT
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rmyoungsc
 Post subject: Re: In isosceles triangle RST what is the measure of angle R?
 Post Posted: Fri Aug 21, 2009 3:50 pm 
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Ok I misunderstood the law. It only applies to the lengths of the sides of a triangle, not the degree measure of the angles in a triangle. thanks
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hakobc
 Post subject: Re: In isosceles triangle RST what is the measure of angle R?
 Post Posted: Fri Aug 28, 2009 2:00 pm 
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rmyoungsc wrote:
Ok I misunderstood the law. It only applies to the lengths of the sides of a triangle, not the degree measure of the angles in a triangle. thanks

I agree with you, but I think if the lengths of the sides of triangle are equal, that means their conrresponding angles are also equal to each other, thus I also don't agree with the original answer choice.
I am stuck on this and I think if 40 gonna be any angle in the isosceles triangle, then you can easily find the rest of angles! please comment if you not agree!
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RonPurewal
 Post subject: Re: In isosceles triangle RST what is the measure of angle R?
 Post Posted: Fri Sep 25, 2009 11:11 pm 
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hakobc wrote:
rmyoungsc wrote:
Ok I misunderstood the law. It only applies to the lengths of the sides of a triangle, not the degree measure of the angles in a triangle. thanks

I agree with you, but I think if the lengths of the sides of triangle are equal, that means their conrresponding angles are also equal to each other, thus I also don't agree with the original answer choice.
I am stuck on this and I think if 40 gonna be any angle in the isosceles triangle, then you can easily find the rest of angles! please comment if you not agree!


incorrect on 2 counts.

first of all, WE DON'T KNOW WHICH TWO ANGLES ARE EQUAL. there are two possibilities for an isosceles triangle with a 40° angle in it:
(case 1) 40°, 40°, 100° (if angle S = 40° is one of the two equal angles)
(case 2) 40°, 70°, 70° (if angle S = 40° is NOT one of the two equal angles)

worse yet - it would still be insufficient even if only case (1) were possible!
this is because there are two DIFFERENT angles - 100° and the other 40° - remaining, and you don't know which of these is angle T. i.e., angle T could still be either 40° or 100° in this case.
so you don't even need to come up with case 2 in order to prove insufficient!
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