Question

given the figure below, find the values of x and z.
(9x + 47)°
(11x + 35)°
z°

Explanation:

Step1: Set up equation for x

Since vertical - angles are equal, we set $9x + 47=11x + 35$.
$9x+47 = 11x + 35$
$47-35=11x - 9x$
$12 = 2x$
$x=\frac{12}{2}=6$

Step2: Find the value of one angle

Substitute $x = 6$ into $9x + 47$.
$9\times6+47=54 + 47=101^{\circ}$

Step3: Find the value of z

The angle $(9x + 47)^{\circ}$ and $z^{\circ}$ are supplementary (linear - pair), so $z=180-(9x + 47)$.
Substitute $x = 6$ into the formula for $z$.
$z=180-(9\times6 + 47)=180 - 101 = 79$

Answer:

$x = 6$
$z = 79$