Let's analyze the geometry in the figure.

1. Vertical Angles: The given angles of 70° and $(11x + 55)^\circ$ are vertical angles, which means they are equal.

   • $70^\circ = (11x + 55)^\circ$

2. Opposite Angles: The $z^\circ$ angle and $70^\circ$ are opposite angles, so they are equal as well:

   • $z = 70^\circ$

Solve for $x$:

We can solve the equation for $x$: $70 = 11x + 55$

Subtract 55 from both sides: $70 - 55 = 11x$ $15 = 11x$

Now, divide both sides by 11: $x = \frac{15}{11} \approx 1.36$

Final values:

• $x \approx 1.36$
• $z = 70^\circ$

Would you like more detailed steps or explanations on any part?

Here are 5 follow-up questions to expand your understanding:

1. What are vertical angles and why are they equal?
2. How are opposite angles in intersecting lines related?
3. Can you apply this concept to find angles in a triangle?
4. What if $x$ represented a different function; how would it change the result?
5. How would you verify that your solution is correct?

Tip: In problems involving intersecting lines, remember that vertical angles are always equal.