The image shows a crossed lines configuration with the following given information:

• One of the angles is labeled as $88^\circ$.
• Two unknown angles $b$ and $c$ need to be found.

This setup involves vertical angles and linear pairs. Here's how we can solve for $b$ and $c$:

1. Vertical Angles:

   • Vertical angles are always congruent (equal). The angle vertically opposite the $88^\circ$ angle is also $88^\circ$. Therefore, $b = 88^\circ$.

2. Linear Pair:

   • Angles on a straight line (linear pair) add up to $180^\circ$. The angle $c$ forms a linear pair with the given $88^\circ$ angle. Thus, $c = 180^\circ - 88^\circ = 92^\circ.$

Final Answers:

• $b = 88^\circ$
• $c = 92^\circ$

Would you like further clarification or a deeper explanation of any step?

Here are some related questions you could explore:

1. What are vertical angles, and why are they always equal?
2. How do linear pairs of angles relate to the concept of supplementary angles?
3. Can you find the sum of angles around a point?
4. How would the solution change if the angle was not on a straight line?
5. How do the properties of parallel lines and transversals relate to these types of angle problems?

Tip: Always check if two angles form a linear pair (add to $180^\circ$) or are vertically opposite (equal) when dealing with crossed lines.