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WXYZ is a kite. If the measure of angle WXY is 120°, the measure of angle WZY is 4x° and the measure of angle ZWX is 10x°, find the measure of angle ZYX.

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jcherry99

Answer:

100 degrees

Step-by-step explanation:

Remark

The endpoints of the smaller diagonal of a kite, intersect the vertexes of 2 equal angles. Put in simpler language, if x is at the top of the kite and x is the vertex of the larger angle between the top and bottom angles, then the other two angles (left and right) are equal.

In still simpler language. <W = <Y

Equation

<X + <W + <Z + <Y = 360               All quadrilaterals have 360 degrees for their interior angles.

Givens

  • <X = 120
  • <W = 10x
  • <Z = 4x
  • <Y = 10x

Solution

  • 120 + 10x + 10x + 4x = 360      Gather like terms on the left
  • 120 + 24x = 360                       Subtract 120 from both sides
  • 120- 120 + 24x = 360 - 120      consolidate
  • 24x = 240
  • x = 10

Answer

  • Since <ZYX = 10x
  • <ZYX = 10*10 = 100 degrees.
Ver imagen jcherry99
NvidiaIntely

Answer:

100

Step-by-step explanation:

Angle ZWX and angle ZYX are congruent.

360 = 120 + 4x + 10x + 10x

360 = 120 + 24x

240 = 24x

10 = x

The measure of angle ZYX is equal to 10(10) = 100°

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