Question

score: 2.75/5 penalty: 0.25 off
question
find the value of ( x ), ( y ), and ( z ) in the rhombus below.
answer attempt 1 out of 2
( x=)( y=)( z=)

Explanation:

Step1: Use the property of opposite angles in a rhombus

In a rhombus, opposite angles are equal.
So, $4x + 9=63$

$$\begin{align*} 4x&=63 - 9\\ 4x&=54\\ x&=\frac{54}{3}\\ x& = 18 \end{align*}$$

Step2: Use the property of adjacent angles in a rhombus

Adjacent angles in a rhombus are supplementary ($\text{sum}=180^{\circ}$).
So, $(4y - 5)+63 = 180$

$$\begin{align*} 4y-5&=180 - 63\\ 4y-5&=117\\ 4y&=117 + 5\\ 4y&=122\\ y&=\frac{122}{4}\\ y& = 16 \end{align*}$$

Step3: Use the property of opposite angles in a rhombus

Opposite angles are equal. So, $2z-7=63$

$$\begin{align*} 2z&=63 + 7\\ 2z&=70\\ z&=\frac{70}{2}\\ z& = 32 \end{align*}$$

Answer:

$x = 18$, $y = 16$, $z = 32$