DS question

winter wrote:In isosceles triangle RST what is the measure of angle R?
1) The measure of angle T is 100
2) The measure of angle S is 40

Answer is A.

How do we know which sides of a triangle are equal?

(1) Angle T = 100. Given that RST is an isosceles triangle and in an isosceles triangle, 2 angles are equal.
But none of the other two angles can be equal to angle T, since the sum of the angles in a triangle is 180º.
It means the other two angles S and R are equal. Let angle S = angle R = x
2x + 100 = 180 implies x = 40. So, angle R = 40º.

So, (1) is SUFFICIENT.

(2) Angle S = 40º, but here angle S can be equal to R or it can be equal to angle T, which is not given.
Hence, (2) is NOT SUFFICIENT.

The correct answer is (A).