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In isosceles triangle XYZ, what is the measure of angle XZY?

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In isosceles triangle XYZ, what is the measure of angle XZY? [#permalink]

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New post 06 Jun 2017, 10:08
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Re: In isosceles triangle XYZ, what is the measure of angle XZY? [#permalink]

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St. 1 - this does not help us identify the angle XZY as the angles of the triangle could be 44-44-92 or 44-68-68. Insufficient.

St. 2 - this states outright that one angle is 92 degrees making it the largest angle of the triangle. Knowing that this is an isosceles triangle, we can conclude that the other two angles sum to 88 and are equal, that is 44. Sufficient.

I think it should be: B

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Re: In isosceles triangle XYZ, what is the measure of angle XZY? [#permalink]

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New post 06 Jun 2017, 11:48
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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 92
ASIDE: 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 degrees
Since 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 degrees
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer:
[Reveal] Spoiler:
B


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Re: In isosceles triangle XYZ, what is the measure of angle XZY? [#permalink]

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New post 15 Jan 2018, 09:53
statement 1 says angle xyz = 44 and we already know that the triangle is an isosceles triangle which means 2 angles have the same degrees. therefore xzy could be 2 possibilities .
xyz = 44 and yxz = 44 then xzy = 180- 44 -44 = 92 alternatively if xyz = 44 then other 2 angles can be 180-44 = 136/2 = 68 degrees no clear answer therefore not sufficient.

Statement 2 says angle yxz measures = 92 . which means no other angle can share its deminsions because if it does it exceeds 180 therefore the other 2 angle = part of isosceles.
zxy = 180-92 = 88/2 =44. sufficient .

Ans = B
Re: In isosceles triangle XYZ, what is the measure of angle XZY?   [#permalink] 15 Jan 2018, 09:53
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In isosceles triangle XYZ, what is the measure of angle XZY?

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