Question

below, k || o. find the values of y and z.

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. The angle vertical to the $82^{\circ}$ angle has a measure of $82^{\circ}$. Since $y^{\circ}$ and the vertical - angle of the $82^{\circ}$ angle are corresponding angles (because $k\parallel o$), $y = 82$.

Step2: Use the relationship of angles

The angle $(6z - 92)^{\circ}$ and the $82^{\circ}$ angle are either corresponding, alternate - interior, or same - side interior angles. Since $k\parallel o$, we can set up an equation based on the angle - relationship. Here, $(6z - 92)^{\circ}$ and the $82^{\circ}$ angle are corresponding angles, so $6z-92 = 82$.
Add 92 to both sides of the equation: $6z=82 + 92$.
$6z=174$.
Divide both sides by 6: $z=\frac{174}{6}=29$.

Answer:

$y = 82$
$z = 29$