In an isosceles triangle two angles must be equal and one different.

1) If one angle is 96 degrees it cannot be one of the two equal angles (because you would have more than 180 degrees) so it must be the different angle and the others must be (180-96)/2 = 42 degrees.

2) If one angle is 42 degree we could have 42,42,96 (as seen in clue one), OR 42 could be the different angle and then the others would be (180-42)/2, giving us 69, 69, 42. Two possibilities = insufficient.

Answer A

Thank you for the quick reply,

If stem one gives 96 degrees, and 96 can only be the non-equal angle, then I cannot assume that it is the largest angle? If 96 was split could you not find the other angles?

You are given 96 as an angle. You cannot split it, you have to have a 96 degree angle in the triangle. By splitting it you would have 2 triangles which is a different problem.

milanproda wrote:Thank you for the quick reply,

If stem one gives 96 degrees, and 96 can only be the non-equal angle, then I cannot assume that it is the largest angle? If 96 was split could you not find the other angles?

Would just like to point out that you don't need the split: if you know that the 96 is non-equal angle (which it must, since we cannot have a twin 96), then the other two angles must be equal. So the remaining 180-96 = 84 is split two ways between the two equal angles, and each is 42.

The problem with (2) is that you do not know whether the 42 angle is one of the equals (leaving the other equal angle as 42 and the last one as 96), or the non-equal angle (leaving the other two angles as half of 180-42=138, or 69). You don't need to split the given angle in order to find the other two: The minute you define your scenario (42 is one of the equals, or the third non-equal), you can find the other two angles without splitting the 42 one. But the problem remains that there are two scenarios: two different triangles that can be drawn, and the required angle DEF will be different for either scenario.