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Elodia [21]
3 years ago
8

Use the diagram to solve for the three variables so that the quadrilateral will be a rhombus. Show all of your work for full cre

dit.

Mathematics
1 answer:
satela [25.4K]3 years ago
3 0

Answer:

  • x = 4
  • y = 4
  • z = 7

Step-by-step explanation:

Each triangle is a right triangle, and all are congruent. So ...

  90 -m∠CAB = (1/2)m∠CDA

  90 -(4x +33) = (1/2)(12x +34)

  57 -4x = 6x +17 . . . . . . . eliminate parentheses

  40 = 10x . . . . . . . . . . . . .add 4x-17

  4 = x

We also have ...

  2m∠CAD = m∠BCD

  2(3z +28) = 10z +28

  6z +56 = 10z +28 . . . . . eliminate parentheses

  28 = 4z . . . . . . . . . . . . . .subtract 6z+28

  7 = z . . . . . . . . . . . . . . . . divide by 4

Since BC = CD ...

  x = y = 4

The values of the three variables are ...

  x = 4, y = 4, z = 7.

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