Question

given the figure below, find the values of x and z.
(12x - 74)°
(14x - 98)°
z°
x = 8
z = 158

Explanation:

Step1: Use vertical - angles property

Vertical angles are equal. So, $12x - 74=14x - 98$.

Step2: Solve for $x$

Subtract $12x$ from both sides: $-74 = 14x-12x - 98$.
This simplifies to $-74 = 2x - 98$.
Add 98 to both sides: $2x=-74 + 98$.
So, $2x = 24$, and $x = 12$.

Step3: Find the value of one of the angles

Substitute $x = 12$ into $12x - 74$.
$12\times12-74=144 - 74=70$.

Step4: Use linear - pair property

The angle $z$ and the angle $12x - 74$ form a linear - pair. A linear - pair of angles sums to $180^{\circ}$.
So, $z+70 = 180$.
Subtract 70 from both sides: $z=180 - 70 = 110$.

Answer:

$x = 12$, $z = 110$