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Find the value of x, y, and z in the rhombus below.

Find The Value Of X Y And Z In The Rhombus Below class=

Sagot :

Solution:

It should be noted:

  • Opposite sides of a rhombus are always equal.
  • Opposite angles of a rhombus are always equal.

Thus:

  • (-y - 10) = 90°
  • 3z - 3 = 90°
  • 4x - 2 = 90°

Finding x:

  • 4x - 2 = 90°
  • => 4x = 90 + 2
  • => 4x = 92
  • => x = 23

Finding y:

  • (-y - 10) = 90°
  • => -y - 10 = 90°
  • => -y = 100
  • => y = -100

Finding z:

  • 3z - 3 = 90°
  • => 3z = 90 + 3
  • => 3z = 93
  • => z = 31

Opposite angles are equal

[tex]\\ \rm\hookrightarrow 90=-y-10[/tex]

[tex]\\ \rm\hookrightarrow -y=90+10[/tex]

[tex]\\ \rm\hookrightarrow y=-100[/tex]

And consecutive angles have some 180

  • So all angles are of 90°

[tex]\\ \rm\hookrightarrow 3z-3=90[/tex]

[tex]\\ \rm\hookrightarrow 3z=93[/tex]

[tex]\\ \rm\hookrightarrow z=31[/tex]

And

[tex]\\ \rm\hookrightarrow 4x-2=90[/tex]

[tex]\\ \rm\hookrightarrow 4x=92[/tex]

[tex]\\ \rm\hookrightarrow 23[/tex]

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