Question

given the figure below, find the values of x and z.
94°
z°
(9x + 22)°

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. So, $9x + 22=94$.

Step2: Solve for $x$

Subtract 22 from both sides of the equation $9x + 22=94$: $9x=94 - 22$, so $9x = 72$. Then divide both sides by 9: $x=\frac{72}{9}=8$.

Step3: Use linear - pair property

The angle $z$ and the $94^{\circ}$ angle form a linear pair. A linear pair of angles is supplementary, so $z + 94=180$.

Step4: Solve for $z$

Subtract 94 from both sides of the equation $z + 94=180$: $z=180 - 94 = 86$.

Answer:

$x = 8$
$z = 86$