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Geometry - Triangles

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Geometry - Triangles

by polter » Mon May 09, 2011 3:11 pm
In isosceles triangle RST, what is the measure of R?
(1) the measure of T = 100
(2) The measure of S = 40.

My logic:
From (1), R + S = 180 - 100 = 80. Since T > 90, angle R = angle S. Hence, R = 80/2 = 40
From (2), R + T = 180 - 40 = 140. Assuming, angle R = angle t. Hence, R = 140/2 = 70.
Hence, C

OA [spoiler]Correct Answer = A[/spoiler]
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by cyrwr1 » Mon May 09, 2011 7:07 pm
Isosceles triange RST means two angles/lengths are equal.

1) you know T is 100, thus angles R and S are 40 = (180-100)/2, another angle besides T cannot be 100
Sufficient
2) Angle S = 40, R and T =140
What are the possibilities of R and T=140? One is 40 and another is 100 OR both R and T are 70.
There are 3 possibilities of what R can be : 40, 70, 100
Insufficient

A is the answer.
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by Anurag@Gurome » Mon May 09, 2011 7:22 pm
polter wrote:In isosceles triangle RST, what is the measure of R?
(1) the measure of T = 100
(2) The measure of S = 40.

My logic:
From (1), R + S = 180 - 100 = 80. Since T > 90, angle R = angle S. Hence, R = 80/2 = 40
From (2), R + T = 180 - 40 = 140. Assuming, angle R = angle t. Hence, R = 140/2 = 70.
Hence, C

OA [spoiler]Correct Answer = A[/spoiler]
In an isosceles triangle, two angle are equal.

(1) angle T = 100º implies the other angle cannot be equal to 100 as the sum of the 3 angles in a triangle is 180º.
This means that angles R and S are equal. So, 2R + 100 = 180 implies 2R = 80 implies R = 40º
So, (1) is SUFFICIENT.

(2) angle S = 40º does not imply that which of the angles are equal.
So, (2) is NOT SUFFICIENT.

The correct answer is A.
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by polter » Tue May 10, 2011 2:55 am
Thanks for your responses.

Learnings:
For DS, there needs to be a unique solution and not multiple solution. Right?
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by Anurag@Gurome » Tue May 10, 2011 3:11 am
polter wrote:Thanks for your responses.

Learnings:
For DS, there needs to be a unique solution and not multiple solution. Right?
You are absolutely right Polter. We need to have a unique answer, only then we can say that a statement is Sufficient.
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by MAAJ » Tue May 10, 2011 1:58 pm
IMO this statement is refering to the length of side R not angle R. So instead it should be: what's is the measure of angle R. IMO this question is incomplete/ambiguous?
polter wrote:In isosceles triangle RST, what is the measure of R?
(1) the measure of T = 100
(2) The measure of S = 40.

My logic:
From (1), R + S = 180 - 100 = 80. Since T > 90, angle R = angle S. Hence, R = 80/2 = 40
From (2), R + T = 180 - 40 = 140. Assuming, angle R = angle t. Hence, R = 140/2 = 70.
Hence, C

OA [spoiler]Correct Answer = A[/spoiler]
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