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The problem involves two angles that form a right angle (90°), where the measures of the two angles are given as:

- \( (4m - 6)^\circ \)
- \( (6m + 6)^\circ \)

Since these two angles form a right angle, their sum must equal \( 90^\circ \). Therefore, we can set up the following equation:

\[
(4m - 6) + (6m + 6) = 90
\]

Let's solve for \( m \).

### Step 1: Simplify the equation
\[
4m - 6 + 6m + 6 = 90
\]
\[
(4m + 6m) + (-6 + 6) = 90
\]
\[
10m = 90
\]

### Step 2: Solve for \( m \)
\[
m = \frac{90}{10}
\]
\[
m = 9
\]

Thus, the value of \( m \) is 9.

Would you like any further clarification on this solution?

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Here are 5 related questions to expand on this concept:
1. How do we determine if two angles are complementary or supplementary?
2. What happens if the sum of the angles exceeds 90° in this type of problem?
3. How would this problem change if one of the angles was an exterior angle?
4. How do you verify the solution using the original angle expressions?
5. What is the relationship between linear pairs of angles and supplementary angles?

**Tip:** Always ensure the sum of the angles aligns with the geometric configuration (e.g., right angles should sum to 90°).

Solve for the value of m, given two angles: (4m - 6)° and (6m + 6)° that form a right angle.

Learn how to solve for m in the given equation where two angles, (4m - 6)° and (6m + 6)°, form a right angle. This problem covers key concepts in algebra and angle relationships. Ideal for students in Grades 9-10.

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