https://file.aiquickdraw.com/mathbot/file/1726565970866uv1xqhq6.jpg

The image presents a geometric diagram, where we need to find the value of \( x \). The setup includes the following:

- Two angles marked as \( (3x + 3)^\circ \) and \( (4x + 3)^\circ \).
- The presence of a right angle (marked with a red square), which indicates that the two angles adjacent to the right angle must sum to \( 90^\circ \).

### Steps to solve:

1. The two angles adjacent to the right angle are:
   \[
   (3x + 3)^\circ \quad \text{and} \quad (4x + 3)^\circ.
   \]
2. Since they form a right angle, their sum must be \( 90^\circ \):
   \[
   (3x + 3) + (4x + 3) = 90.
   \]
3. Simplify the equation:
   \[
   3x + 4x + 3 + 3 = 90,
   \]
   \[
   7x + 6 = 90.
   \]
4. Subtract 6 from both sides:
   \[
   7x = 84.
   \]
5. Solve for \( x \):
   \[
   x = \frac{84}{7} = 12.
   \]

### Solution:
The value of \( x \) is \( \boxed{12} \).

Would you like more details on this, or do you have any questions?

Here are some related questions to explore further:
1. What is the measure of the two angles in degrees when \( x = 12 \)?
2. How do vertical angles relate to this problem?
3. Can you use the concept of supplementary angles to solve this problem in another way?
4. What if the given angles were external angles of a polygon—how would that affect the calculation?
5. How can you determine if two lines are perpendicular based on their angle measurements?

**Tip:** Always check if angles form complementary or supplementary pairs when dealing with right angles.

Find the value of x in the given geometric diagram, where the angles are (3x + 3)° and (4x + 3)°, with the presence of a right angle.

In this problem, we solve for x in a geometric diagram where two angles, (3x + 3)° and (4x + 3)°, are complementary and sum to 90°. This problem involves algebra and the complementary angles theorem. Suitable for students in Grades 8-10.

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