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The image shows a problem related to vertical, adjacent, and complementary angles. The diagram has an angle labeled as 123° and two unknown angles, \( b \) and \( c \), that you need to find.

### Step-by-step solution:

1. **Identifying the angles:**
   - Angle \( b \) and the 123° angle are **vertical angles**, meaning they are equal.
     \[
     b = 123^\circ
     \]
   
2. **Finding angle \( c \):**
   - Angle \( c \) and the 123° angle are **adjacent angles** forming a straight line, meaning they are supplementary. The sum of supplementary angles is 180°.
     \[
     c + 123^\circ = 180^\circ
     \]
     Solving for \( c \):
     \[
     c = 180^\circ - 123^\circ = 57^\circ
     \]

### Final Answer:
- \( b = 123^\circ \)
- \( c = 57^\circ \)

Would you like further details on this solution or clarification on any part?

Here are 5 related questions to explore further:
1. What are complementary angles, and how do they differ from supplementary angles?
2. How do vertical angles relate to each other in different geometric configurations?
3. Can two adjacent angles ever be complementary? If so, under what conditions?
4. How can you determine if a set of angles forms a linear pair?
5. What is the difference between adjacent and non-adjacent supplementary angles?

**Tip:** When dealing with angles around a point or straight lines, always check for vertical and supplementary angle relationships!

Find the measure of the missing angles. The diagram shows an angle of 123° with two unknown angles b and c.

Learn how to find the missing angles using vertical and supplementary angles. In this problem, an angle of 123° is given, and you are tasked with finding the other angles. Suitable for Grades 6-8 students.

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