In this image, we see two intersecting lines, which form four angles. One of the angles is given as $118^\circ$, and we need to find the measures of the missing angles, marked as $b$ and $c$.

To solve this:

1. Vertical angles are equal: When two lines intersect, the opposite angles (vertical angles) are congruent. Thus, the angle opposite $118^\circ$, which is angle $b$, must also be: $b = 118^\circ$

2. Linear pairs add up to 180°: The angles that are adjacent (next to each other) on a straight line form a linear pair, and their measures add up to $180^\circ$. Therefore, angle $c$ and angle $118^\circ$ are a linear pair, so: $c + 118^\circ = 180^\circ$ Solving for $c$: $c = 180^\circ - 118^\circ = 62^\circ$

So, the missing angles are:

• $b = 118^\circ$
• $c = 62^\circ$

Would you like more details on how these properties work, or do you have any other questions?

Follow-up questions:

1. What are vertical angles, and why are they equal?
2. Can you explain what a linear pair of angles is?
3. How do complementary and supplementary angles differ?
4. Are there any exceptions to these rules when angles are in different types of polygons?
5. How would this change if the given angle were part of a triangle?

Tip:

Always remember that vertical angles are congruent (equal), and linear pairs always add up to 180°. These properties are key to solving problems involving intersecting lines.