BTGmoderatorDC 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°.
OA A
Source: GMAT Prep
We know that for an isosceles triangle, two angles are equal. Thus, two angles of ∆RST are equal. We have to find out the measure of angle R.
(1) The measure of ∠T is 100°.
Since ∠T = 100°, the sum of the other two angles ∠S and ∠R = 180 - 100 = 80º. The two equal angles can be ∠S and ∠R since if ∠T = 100º and one between ∠R and ∠S are equal, the sum of the three angles would exceed 200, which is not possible. Thus, we have ∠S = ∠R = 80/2 = 40º. Sufficient.
(2) The measure of ∠S is 40°.
Case 1: Say ∠S = ∠R = 40; thus, ∠T = 180 - 40*2 = 100º.
Case 2: Say ∠S = ∠T = 40; thus, ∠R = 180 - 40*2 = 100º.
No unique answer. Insufficient.
The correct answer:
A
Hope this helps!
-Jay
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