Bunuel wrote:
In isosceles triangle XYZ, what is the measure of angle XZY?
(1) Angle XYZ measures 44 degrees.
(2) Angle YXZ measures 92 degrees.
Target question: What is the measure of angle XZY? Given: Triangle XYZ is isosceles So, 2 of the angles are equal.
Statement 1: Angle XYZ measures 44 degrees There are two possible cases that satisfy statement 1:
Case a: angle XYZ is one of the two angles that are equal, which means the 3 angles are 44, 44 and 92. In this case,
angle XZY can be EITHER 44 or 92ASIDE: At this point, we can already conclude that statement 1 is not sufficient. However, let's examine the other case, for "fun"
Case b: angle XYZ is NOT one of the two angles that are equal, which means the 3 angles are 44, 68 and 68. In this case,
angle XZY can be 68 degreesSince we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: Angle YXZ measures 92 degrees. From this information, we can be certain that
angle YXZ is NOT one of the two angles that are equal.
We know this because, if two angles were to equal 92 degrees, then the sum of those angles would be 184 degrees, and the 3 angles in a triangle add to 180 degrees.
So, it must be the case that the other two angles are equal.
This means the 3 angles are 44, 44 and 92. In this case,
angle XZY must be 44 degreesSince we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer:
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