Question

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

Answer 1

Opposite angles are equal

$\\ \rm\hookrightarrow 90=-y-10$

$\\ \rm\hookrightarrow -y=90+10$

$\\ \rm\hookrightarrow y=-100$

And consecutive angles have some 180

• So all angles are of 90°

$\\ \rm\hookrightarrow 3z-3=90$

$\\ \rm\hookrightarrow 3z=93$

$\\ \rm\hookrightarrow z=31$

And

$\\ \rm\hookrightarrow 4x-2=90$

$\\ \rm\hookrightarrow 4x=92$

$\\ \rm\hookrightarrow 23$

Answer 2

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