https://file.aiquickdraw.com/mathbot/file/1729379874775yncyar93.jpg

To help solve the problem shown in the image, we need to break down the relevant parts:

1. **Find the value of \( x \):**
   - You are correct that \( x = 7 \). This has already been solved.

2. **Solve for \( \angle CBA \):**
   - The triangle formed is \( \triangle ABC \), and we are dealing with the angles inside and outside of this triangle.
   - The exterior angle \( \angle DCB \) is equal to the sum of the two non-adjacent interior angles of the triangle.
   
   Using the information from the diagram:
   - The exterior angle \( \angle DCB = (9x + 2)^\circ \).
   - The interior angles \( \angle ABC = (x + 17)^\circ \) and \( \angle BAC = (3x + 20)^\circ \).

   According to the exterior angle theorem:
   \[
   \angle DCB = \angle ABC + \angle BAC
   \]
   Substitute the expressions:
   \[
   (9x + 2) = (x + 17) + (3x + 20)
   \]
   Simplify the equation:
   \[
   9x + 2 = x + 17 + 3x + 20
   \]
   Combine like terms:
   \[
   9x + 2 = 4x + 37
   \]
   Now, solve for \( x \):
   \[
   9x - 4x = 37 - 2
   \]
   \[
   5x = 35
   \]
   \[
   x = 7
   \]
   
   Now that \( x = 7 \), we can substitute it back into the expression for \( \angle CBA \):
   \[
   \angle CBA = x + 17 = 7 + 17 = 24^\circ
   \]

Thus, \( \angle CBA = 24^\circ \).

Let me know if you would like more clarification or further details.

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**Additional Questions:**
1. What is the exterior angle theorem, and how is it used in this problem?
2. Can you explain why \( \angle CBA \) cannot be \( 102^\circ \)?
3. How would you calculate the remaining angle \( \angle BAC \) after finding \( x \)?
4. What is the sum of the interior angles of a triangle, and how does that apply here?
5. Can we verify our solution by checking the sum of all angles around point \( C \)?

**Tip:** Always check your exterior angle theorem calculations by verifying the sum of interior angles equals 180°.

Find the value of x and solve for ∠CBA using the given triangle with exterior angle DCB.

In this problem, we use the exterior angle theorem to find the value of x and solve for ∠CBA in a triangle. The exterior angle is equal to the sum of the two non-adjacent interior angles. This detailed solution is suitable for students in Grades 8-10.

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