https://file.aiquickdraw.com/mathbot/file/1724160462458opaut52d.jpg

10. In figure, ∠AOC and ∠BOC form a linear pair. If a – 2b = 30°,
find a and b?

To solve the problem, let's analyze the given figure and the information provided:

### Given:
- \(\angle AOC\) and \(\angle BOC\) form a linear pair.
- \(a - 2b = 30^\circ\)

### Key Concept:
- Angles that form a linear pair are supplementary, meaning their sum is \(180^\circ\).

### Step-by-Step Solution:
1. **Identify the angles:**
   - Let \(\angle AOC = a\) and \(\angle BOC = b\).
   
2. **Set up the supplementary angle equation:**
   - Since \(\angle AOC\) and \(\angle BOC\) are supplementary:
     \[
     a + b = 180^\circ
     \]

3. **Use the given equation:**
   - You are also given that:
     \[
     a - 2b = 30^\circ
     \]

4. **Solve the system of equations:**
   - We have two equations:
     1. \(a + b = 180^\circ\)
     2. \(a - 2b = 30^\circ\)
     
   - To solve for \(a\) and \(b\), we can use the substitution or elimination method. I'll use the elimination method here:
   
   - From the first equation:
     \[
     a = 180^\circ - b
     \]
   - Substitute this into the second equation:
     \[
     (180^\circ - b) - 2b = 30^\circ
     \]
     \[
     180^\circ - 3b = 30^\circ
     \]
     \[
     3b = 150^\circ
     \]
     \[
     b = 50^\circ
     \]
     
   - Now, substitute \(b = 50^\circ\) back into the first equation:
     \[
     a + 50^\circ = 180^\circ
     \]
     \[
     a = 130^\circ
     \]

### Final Answer:
- \(a = 130^\circ\)
- \(b = 50^\circ\)

Would you like more details or have any questions about this solution?

### Follow-up Questions:
1. What is the sum of angles in a linear pair?
2. Can you generalize the relationship between angles that form a linear pair?
3. How would the solution change if the angles were given in radians instead of degrees?
4. What would happen if the equation was \(a + 2b = 30^\circ\) instead?
5. Can you explain how the elimination method works for solving linear equations?

### Tip:
When dealing with linear pairs or angles on a straight line, always remember that their sum is \(180^\circ\), which is a helpful check for your calculations.

Explore how to find angles AOC and BOC forming a linear pair, given the equation a - 2b = 30°. Learn the step-by-step solution and understand the concept of linear pairs and supplementary angles. Suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation