Question

given the figure below, find the values of x and z.
(12x - 74)°
(14x - 90)°
z°
x =
z =

Explanation:

Step1: Set up equation using vertical - angle property

Vertical angles are equal. So, $12x - 74=14x - 90$.

Step2: Solve for x

Subtract $12x$ from both sides: $-74 = 14x-12x - 90$, which simplifies to $-74 = 2x-90$. Then add 90 to both sides: $-74 + 90=2x$, so $16 = 2x$. Divide both sides by 2: $x=\frac{16}{2}=8$.

Step3: Find the value of one of the angles

Substitute $x = 8$ into $12x - 74$: $12\times8-74=96 - 74 = 22$.

Step4: Find z

Since the angle $z$ and the angle $(12x - 74)$ are supplementary (they form a straight - line, so their sum is 180°), then $z=180-(12x - 74)$. Substituting $x = 8$ gives $z=180 - 22=158$.

Answer:

$x = 8$
$z = 158$