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In the given figure, ∠UVZ = 84o. IF XY = VY = VZ, find the value of an

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In the given figure, ∠UVZ = 84o. IF XY = VY = VZ, find the value of an  [#permalink]

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New post 28 Apr 2020, 07:41
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Screenshot 2020-04-28 at 9.11.02 PM.png [ 32.12 KiB | Viewed 537 times ]


In the given figure, ∠UVZ = 84 degrees. IF XY = VY = VZ, find the value of angle YVZ.

A. 21
B. 32
C. 42
D. 68
E. 72
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Re: In the given figure, ∠UVZ = 84o. IF XY = VY = VZ, find the value of an  [#permalink]

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New post 28 Apr 2020, 08:01
Since VY and VZ are equal, the triangle is iscosceles and angle VYZ=angle VZY=k (suppose).

Applying Exterior Angle theroem to Triangle VXZ, angleVXY+k=84.

So, angleVXY=angleVXY (since sides XY=VY) and they are both equal to 84-k.

Now, sum of angles VXY,VYX and XVY must be 180. Equate to get k=56.

Now, x=180-(84-56)-84=68.
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Re: In the given figure, ∠UVZ = 84o. IF XY = VY = VZ, find the value of an  [#permalink]

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New post 28 Apr 2020, 11:24
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Suppose ∠VXY = x

Since XY = VY, ∠XVY = x.

Now ∠VYZ = ∠VXY+ ∠XVY = 2x

Since VZ = VY, ∠VZY =2x.

x+2x = 84

x= 28

angle YVZ = 180-4*28= 68



Kritisood wrote:
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In the given figure, cUVZ = 84 degrees. IF XY = VY = VZ, find the value of angle YVZ.

A. 21
B. 32
C. 42
D. 68
E. 72

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Intern
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In the given figure, ∠UVZ = 84o. IF XY = VY = VZ, find the value of an  [#permalink]

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New post 28 May 2020, 22:04
nick1816 wrote:
Suppose ∠VXY = x

Since XY = VY, ∠XVY = x.

Now ∠VYZ = ∠VXY+ ∠XVY = 2x

Since VZ = VY, ∠VZY =2x.

x+2x = 84

x= 28

angle YVZ = 180-4*28= 68



Kritisood wrote:
Attachment:
Screenshot 2020-04-28 at 9.11.02 PM.png


In the given figure, cUVZ = 84 degrees. IF XY = VY = VZ, find the value of angle YVZ.

A. 21
B. 32
C. 42
D. 68
E. 72



Is the "Now ∠VYZ = ∠VXY+ ∠XVY = 2x" part by the exterior angle theorem?
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In the given figure, ∠UVZ = 84o. IF XY = VY = VZ, find the value of an   [#permalink] 28 May 2020, 22:04

In the given figure, ∠UVZ = 84o. IF XY = VY = VZ, find the value of an

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