Question

hallar los valores de x y z.

Explanation:

Step1: Use vertical - angles property

Vertical angles are equal. So, $9x - 84=102$.

Step2: Solve for $x$

Add 84 to both sides of the equation: $9x=102 + 84$, so $9x=186$. Then divide both sides by 9: $x=\frac{186}{9}=\frac{62}{3}\approx20.67$.

Step3: Use linear - pair property

The pair of angles $z$ and $102^{\circ}$ form a linear - pair, so $z + 102=180$.

Step4: Solve for $z$

Subtract 102 from both sides: $z=180 - 102 = 78$.

Answer:

$x=\frac{62}{3}$, $z = 78$