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

[BTGmoderatorDC]

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.

OA A

Source: GMAT Prep

[Jay@ManhattanReview]

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.

OA A

Source: GMAT Prep

Let's take each statement one by one.

(1) The measure of angle T is 100 degrees.

Case 1: Say angle S = angle R. Since angle T = 100, the sum of angle T and angle S = 180 - 100 = 80. This means that angle S = angle R = 40.
Case 2: Say angle T = angle R = 100. But this case is not possible since the sum of two angles 200 (= 100 + 100) > sum of all the angles of a triangle (= 180). Invalid.

Any other case is not possible. Sufficient.

(2) The measure of angle S is 40 degrees.

Case 1: Say angle S = angle R = 40. Thus, angle T = 180 - 40 - 40 = 100. A valid case.
Case 2: Say angle S = angle T = 40. Thus, angle R = 180 - 40 - 40 = 100. A valid case.

No unique value of angle R. Insufficient.

The correct answer: A

Hope this helps!

-Jay
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