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In isosceles triangle XYZ above, angle XYZ measures 100 degrees. What

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In isosceles triangle XYZ above, angle XYZ measures 100 degrees. What [#permalink]

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New post 15 Apr 2018, 09:44
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In isosceles triangle XYZ above, angle XYZ measures 100 degrees. What is the measure of angle XZY?

A. 40
B. 45
C. 60
D. 100
E. Cannot be determined


[Reveal] Spoiler:
Attachment:
Triangle_X_Y_Z.png
Triangle_X_Y_Z.png [ 9.72 KiB | Viewed 203 times ]
[Reveal] Spoiler: OA

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Re: In isosceles triangle XYZ above, angle XYZ measures 100 degrees. What [#permalink]

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New post 15 Apr 2018, 09:51
In an isosceles triangle, 2 sides are equal and hence 2 angles are equal.
Now As angle Y = 100, it is the non equal angle, as we cant have two 100 angles in a triangle because, sum will exceeds the total sum of 180.
Sum of angles in a triangle = 180.
so the other two angles are equal say x.
x+x+100 = 180
2x= 80
x =40. Angle XZY = 40
Answer = A
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Re: In isosceles triangle XYZ above, angle XYZ measures 100 degrees. What [#permalink]

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New post 15 Apr 2018, 09:55
Bunuel wrote:
Image
In isosceles triangle XYZ above, angle XYZ measures 100 degrees. What is the measure of angle XZY?

A. 40
B. 45
C. 60
D. 100
E. Cannot be determined


[Reveal] Spoiler:
Attachment:
Triangle_X_Y_Z.png


We'll show two solutions:

The first is a Logical approach, based on the general properties of triangles.
An isosceles triangle has two equal angles. Since our triangle cannot have two angles equal to 100 (as then the sum of its angles would be more than 180) then 100 must be the angle of the head of the triangle and the two base angles are (180 - 100)/2 = 40.
(A) is our answer.

Another approach is Alternative: since the possible options are right in front of us, why not use them?
If A. were true then one angle would be 100, the other 40 so the last is 180 - 40 -100 = 40 and the triangle is isosceles.
Could work, let's check the others.
If B. were true then the third angle is 180 - 45 - 100 = 35 and the triangle is not isosceles. No.
If C were true then the third angle is 180 - 60 - 100 = 20 and the triangle is not isosceles. No.
If D. were true then the third angle is 180 - 100 - 100 <0 which is impossible. No.
We've tried all the given options and should feel comfortable selecting (A).
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Re: In isosceles triangle XYZ above, angle XYZ measures 100 degrees. What   [#permalink] 15 Apr 2018, 09:55
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In isosceles triangle XYZ above, angle XYZ measures 100 degrees. What

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