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The problem states that ∠A and ∠B are complementary, and ∠A and ∠C are supplementary. It also provides the value of the measure of ∠A as 42° and asks for the measures of ∠B and ∠C.

Here’s how to approach it:

### Step 1: Complementary Angles (∠A and ∠B)
- Complementary angles add up to 90°. Since ∠A and ∠B are complementary:
  \[
  m∠A + m∠B = 90°
  \]
  Given \( m∠A = 42° \), we can solve for \( m∠B \):
  \[
  42° + m∠B = 90°
  \]
  \[
  m∠B = 90° - 42° = 48°
  \]
  
### Step 2: Supplementary Angles (∠A and ∠C)
- Supplementary angles add up to 180°. Since ∠A and ∠C are supplementary:
  \[
  m∠A + m∠C = 180°
  \]
  Given \( m∠A = 42° \), we can solve for \( m∠C \):
  \[
  42° + m∠C = 180°
  \]
  \[
  m∠C = 180° - 42° = 138°
  \]

### Final Answer:
- \( m∠B = 48° \)
- \( m∠C = 138° \)

Would you like more details or further clarifications?

Here are five related questions to explore:
1. What is the definition of complementary angles?
2. How do you determine the value of an unknown angle when given a complementary angle pair?
3. What is the difference between complementary and supplementary angles?
4. If \( m∠A \) were 60°, what would \( m∠B \) and \( m∠C \) be?
5. How can these angle relationships be applied in geometry problems involving polygons?

**Tip:** Complementary angles always add up to 90°, while supplementary angles sum to 180°.

If m∠A = 42°, find m∠B and m∠C given that ∠A and ∠B are complementary, and ∠A and ∠C are supplementary.

Learn how to find the measures of complementary and supplementary angles when m∠A is 42°. This math problem covers key geometry concepts and is suitable for students in Grades 6-8.

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