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In isosceles triangle RST, if angle RST=40 degrees, then what is the sum of the two identical angles in the triangle: is it greater than 120, less than 120, equal to 120 or cannot be determined?

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4 Answers


It's a trick question because there are two possible triangles that meet the conditions of the problem, 40-70-70 and 40-100-40. So the answer is "cannot be determined". This was a GRE question, as always with ETS material you need to be very suspicious of the "obvious answer" and make sure that there is not another possible solution you did not see. I got this one correct.

Anonymous on


First commenter to second commenter: Dude, did you even read what I wrote? Isosceles triangles have two identical angles, and one other angle. The problem, as written, does not tell you which type angle RST is; it just tells you that it is equal to 40 degrees. If it is the other (third) angle, then there are 140 degrees left for the two identical angles, so the triangle must be 40-70-70. In that case the answer is indeed "greater than 120". But if angle RST is instead one of the two identical angles, then the other identical angle must also be 40, so the third angle must be 100. Therefore the triangle is 100-40-40 and the answer is "less than 120". Because two answers are possible with the information given, the answer can ONLY be "cannot be determined". If you still doubt this, then get a protractor out and draw the two triangles, 40-70-70 and 100-40-40, then label a 40 degree angle RST in each, then satisfy yourself that the two identical angles equal 140 in the first case and 80 in the second. If you're still not convinced then I give up. Note that in my original post I clearly said "I got the question right", that means Varsity considered my answer correct.

Anonymous on


Third commenter responding to person who wrote the first and third comment. You are absolutely correct. When I read it I thought the answer was greater than 120 because the sum of all angles in a triangle is 180 degrees. But when I read it again I happened to have missed the word "identical". Adding congruent angles in both hypothetical situations generates different answers. So the last option would indeed be correct.

Anonymous on


Actually to the answerer above, the answer is "greater than 120".

Anonymous on

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