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mlane25269
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the triangle is isosceles, meaning that two of the angles are identical. (the third angle may or may not be identical to the other two; equilateral triangles are also classified as isosceles.)
a little vocabulary to make this easier:
the vertex angle is the angle that's not necessarily equal to the other ones.
the base angles are the two equal angles.
here's the deal: if you know any one of the angles, and you know whether it's the vertex angle or one of the base angles, then you can find all the other angles. (if the vertex angle is X degrees, then each base angle is (180 - X)/2 degrees; if a base angle is X degrees, then the vertex angle is (180 - 2X) degrees.)
statement (1)
this can't be one of the base angles, because you can't have two 100 degree angles in the same triangle. therefore, this is the vertex angle, and each base angle is 40 degrees. sufficient.
statement (2)
you don't know whether this is a base angle or the vertex angle.
if it's the vertex angle, then each base angle (including the desired angle R) is 70 degrees.
if it's a base angle, then the other base angle (which could be angle R) is also 40 degrees, and the vertex angle (which could also be angle R) is 100 degrees.
insufficient.
answer = a
