Question

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

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. So, $z = 75^{\circ}$ since the angle with measure $z^{\circ}$ and the $75^{\circ}$ angle are vertical angles.

Step2: Set up an equation for $x$

The angle with measure $(13x + 70)^{\circ}$ and the $75^{\circ}$ angle are vertical angles, so $13x+70 = 75$.
Subtract 70 from both sides: $13x=75 - 70$, which simplifies to $13x = 5$.
Then divide both sides by 13: $x=\frac{5}{13}$.

Answer:

$x=\frac{5}{13}$, $z = 75$