Question

given the figure below, find the values of x and z.

(9x + 79)°
(5x + 59)°
z°
x =
z =

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. So, $5x + 59=9x + 79$.

Step2: Solve for $x$

Subtract $5x$ from both sides: $59 = 4x+79$. Then subtract 79 from both sides: $59 - 79=4x$, so $- 20 = 4x$. Divide both sides by 4: $x=-5$.

Step3: Find the measure of one of the angles

Substitute $x = - 5$ into $5x + 59$. We get $5\times(-5)+59=-25 + 59 = 34^{\circ}$.

Step4: Use the linear - pair property

The angle $z$ and the angle $5x + 59$ (which is $34^{\circ}$) form a linear - pair. So $z+34 = 180$. Then $z=180 - 34=146^{\circ}$.

Answer:

$x=-5$
$z = 146$