Question

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

Answer 1

x = 15

y = -99

z = -10

Explanation:

In a rhombus, opposite angles are equal.

Knowing this, we can establish the following equation:

`\begin{gathered} -y-7=92 \\ \text{ we solve for y:} \\ y=-92-7 \\ y=-99 \end{gathered}`

The sum of the angles inside a rhombus is equal to 360°, knowing this, we can calculate the missing angle, since both are equal, just like this:

`\begin{gathered} 92+92+\theta+\theta=360 \\ 2\theta=360-92-92 \\ \theta=(176)/(2) \\ \theta=88\degree \\ \\ \text{ therefore:} \\ 6x-2=88 \\ 6x=88+2 \\ 6x=90 \\ x=(90)/(6) \\ x=15 \\ \\ -9z-2=88 \\ -9z=88+2 \\ -9z=90 \\ z=(90)/(-9) \\ z=-10 \end{gathered}`