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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # In the given figure, ∠UVZ = 84o. IF XY = VY = VZ, find the value of an

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Director  P
Joined: 21 Feb 2017
Posts: 621
In the given figure, ∠UVZ = 84o. IF XY = VY = VZ, find the value of an  [#permalink]

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5 00:00

Difficulty:   55% (hard)

Question Stats: 60% (03:27) correct 40% (03:08) wrong based on 43 sessions

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Attachment: 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
Intern  B
Joined: 23 Mar 2020
Posts: 3
Re: In the given figure, ∠UVZ = 84o. IF XY = VY = VZ, find the value of an  [#permalink]

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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.
DS Forum Moderator V
Joined: 19 Oct 2018
Posts: 1987
Location: India
Re: In the given figure, ∠UVZ = 84o. IF XY = VY = VZ, find the value of an  [#permalink]

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2
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:
The attachment Screenshot 2020-04-28 at 9.11.02 PM.png is no longer available

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

Attachments Untitled.png [ 7.31 KiB | Viewed 472 times ]

Intern  B
Joined: 26 Nov 2019
Posts: 6
Location: Sweden
Concentration: Finance, Accounting
GMAT 1: 660 Q40 V40 GPA: 3.6
In the given figure, ∠UVZ = 84o. IF XY = VY = VZ, find the value of an  [#permalink]

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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? 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  