From the given image, we can observe the following:

1. A pair of intersecting lines forms four angles.
2. One of the angles is labeled $80^\circ$, and the two unknown angles are $b$ and $c$.

Step-by-Step Solution:

Step 1: Understanding Vertical Angles

• Opposite (vertical) angles are always equal.
• Therefore: $b = 80^\circ$

Step 2: Adjacent Angles are Supplementary

• Adjacent angles on a straight line sum up to $180^\circ$.
• For angle $c$: $c + b = 180^\circ$ Substituting $b = 80^\circ$: $c + 80^\circ = 180^\circ$ $c = 180^\circ - 80^\circ = 100^\circ$

Final Answer:

$b = 80^\circ, \quad c = 100^\circ$

Let me know if you'd like further clarification or additional examples! Here are some related questions for practice:

1. What are vertical angles, and why are they equal?
2. What is the definition of supplementary angles?
3. How many degrees are in a full rotation of intersecting lines?
4. How do you solve problems involving multiple intersecting lines?
5. Can adjacent angles ever be equal on a straight line?

Tip: Always look for relationships like vertical angles and supplementary angles in intersecting lines to simplify angle calculations!