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To solve for \(m\) in this problem, we need to use the fact that the two angles form a linear pair and therefore sum up to 180 degrees. The given angles are \((4m + 6)^\circ\) and \((5m + 3)^\circ\).

Since they form a straight line, we have:
\[
(4m + 6) + (5m + 3) = 180
\]

Simplifying this equation:
\[
4m + 5m + 6 + 3 = 180
\]

Combine like terms:
\[
9m + 9 = 180
\]

Subtract 9 from both sides:
\[
9m = 171
\]

Divide by 9:
\[
m = 19
\]

Therefore, the value of \(m\) is 19. If you have any questions or need further details, feel free to ask!

Here are 5 related questions to expand your understanding:

1. What are the specific angles when \( m = 19 \)?
2. How do you solve for \(m\) if the angles were given as \((3m + 10)^\circ\) and \((4m - 5)^\circ\)?
3. What is a linear pair of angles?
4. How do you verify that two angles form a linear pair?
5. What is the difference between complementary and supplementary angles?

**Tip:** Always check your solutions by substituting the found value back into the original equation to ensure the angles add up correctly.

Solve for m given two angles (4m + 6)° and (5m + 3)° forming a linear pair.

Learn how to solve a linear pair of angles problem using algebra. The two angles are (4m + 6)° and (5m + 3)° and form a straight line summing up to 180°. Step-by-step solution provided. Suitable for Grades 8-10.

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