Bunuel wrote:
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
Breaking Down the Info:> Set \(\angle X = x\). Since XY = VY, we have \(\angle XVY = x\) as well.
> \(\angle VYZ\) is a supplementary angle, so we have \(\angle VYZ = \angle X + \angle XVY = 2x\).
> \(\angle YVZ = 180 - 4x\) since YVZ is an iscoeles triangle.
> Finally, on line XU we have \(\angle XVY + \angle YVZ + 84 = 180\), which is \(x + 180 - 4x + 84 = 180\).
> \(3x = 84\) and \(x = 28\). We are looking for \(\angle YVZ = 180 - 4x = 180 - 112 = 68\)
Answer: D _________________
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