Let's solve for $x$ and $z$.

Step 1: Identify Angle Relationships

The diagram shows two intersecting lines, forming vertical angles.

1. The given angle $95^\circ$ and the unknown angle $z^\circ$ are vertical angles, meaning: $z = 95^\circ$

2. The other equation involves the expression $(6x - 5)^\circ$, which is vertically opposite the angle labeled $y^\circ$ (though not explicitly labeled, we can infer its value using a straight-line relationship).

Since angles on a straight line add up to $180^\circ$, we set up the equation: $(6x - 5) + 95 = 180$

Step 2: Solve for $x$

$6x - 5 = 85$

$6x = 90$

$x = 15$

Final Answers:

$x = 15, \quad z = 95$

Would you like further clarification? Here are some related questions:

1. What are vertical angles, and why are they always equal?
2. How do linear pairs of angles relate to a straight line?
3. Can we use another method to verify our answer?
4. What if another variable was introduced? How would we solve it?
5. How does this problem relate to real-world geometry applications?

Tip: Always look for vertical and linear pair relationships when dealing with intersecting lines!