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.