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

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

by Gmat_mission » Sun Sep 12, 2021 8:15 am

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

(1) The measure of $$\angle T$$ is $$100^{\circ}.$$

(2) The measure of $$\angle S$$ is $$40^{\circ}.$$

Source: GMAT Paper Tests

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Re: In isosceles triangle $$RST,$$ what is the measure of angle $$R?$$

by [email protected] » Sun Sep 12, 2021 9:33 am

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Gmat_mission wrote:
Sun Sep 12, 2021 8:15 am
In isosceles triangle $$RST,$$ what is the measure of angle $$R?$$

(1) The measure of $$\angle T$$ is $$100^{\circ}.$$

(2) The measure of $$\angle S$$ is $$40^{\circ}.$$

Source: GMAT Paper Tests
IMPORTANT: In an isosceles triangle there are 2 IDENTICAL angles, and 1 LONE angle.

Target question: What is measure of ∠R?

Statement 1: ∠T = 100 degrees
We should recognize that ∠T CANNOT be one of the identical angles. If this were the case, we'd have two angles with measures of 100 degrees each, which would result in a triangle in which the sum of the angles is GREATER than 180 degree (which is IMPOSSIBLE)
So, we can conclude that ∠T must be the LONE angle, which means ∠R and ∠S are the two IDENTICAL angles.
Since the sum of the 3 angles must be 180, we can conclude that ∠R = 40, ∠S = 40, and ∠T = 100
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: ∠S = 40 degrees
Here are two possible cases to consider:
Case a: ∠S is the LONE angle, in which case the ∠R = 70, ∠S = 40, and ∠T = 70
Case b: ∠S is one of the IDENTICAL angles, in which case we could have ∠R = 40, ∠S = 40, and ∠T = 100
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT