Question

given the figure below, find the values of x and z.
85°
(10x - 85)°
z°
x=
z=

Explanation:

Step1: Find the value of \( x \)

Vertical angles are equal. So, \( 10x - 85=85 \).

$$\begin{align*} 10x-85&=85\\ 10x&=85 + 85\\ 10x&=170\\ x&=\frac{170}{10}\\ x& = 17 \end{align*}$$

Step2: Find the value of \( z \)

Adjacent angles form a linear - pair (sum to \( 180^{\circ} \)). So, \( z+85 = 180 \).

$$\begin{align*} z+85&=180\\ z&=180 - 85\\ z&=95 \end{align*}$$

Answer:

\( x = 17 \)
\( z = 95 \)