Respuesta :

The value of x+y+z = 93

Explanation:

angle 1 = 18x

angle 2 = x+y

angle 3 = 30z

In rhombus, the diagonals intersect at 90°

Therefore,

angle 1 : 18x = 90

                  x = 90/18 = 5

angle 2: x+y = 90

              5+y = 90

                  y = 85

angle 3: 30z = 90

                   z = 90/30 = 3

Value of x+y+z = 5+85+3 = 93

Thus, the value of x+y+z = 93

             

The value of x+y+z = 93

Given:

angle 1 = 18x

angle 2 = x+y

angle 3 = 30z

To find:

x+y+z =?

A rhombus is a quadrilateral with both pairs of opposite sides parallel and all sides the same length. In rhombus, the diagonals intersect at 90°

Therefore,

angle 1 :

[tex]18x = 90\\\\ x = \frac{90}{18} \\\\ x= 5 [/tex]

angle 2:

[tex]x+y = 90\\\\ 5+y = 90\\\\ y = 85 [/tex]

angle 3:

[tex]30z = 90\\\\ z =\frac{90}{30} \\\\ z= 3 [/tex]

Value of [tex] x+y+z = 5+85+3 = 93[/tex]

Thus, the value of x+y+z = 93

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