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Let's analyze the given problem step by step to solve for the required values.

The problem provides the following details:

1. \( m \angle DBC = m \angle CAD \)
2. \( m \angle DBA = m \angle CAB \)
3. \( EC = ED \)
4. \( m \angle CBA = 5x + 2 \)
5. \( EC = 3 \), \( EB = 8 \)

The goal is to find:

- \( m \angle DBC \)
- \( m \angle CBA \)
- \( m \angle CAB \)

Looking at the figure, we can see that the values for some angles are expressed in terms of \( x \). There are also other relationships that need to be solved based on the figure and the given conditions.

### Step 1: Solving for \( x \)
From the diagram:
- The angle \( m \angle CBA = 5x + 2 \)
- One of the angles \( m \angle B = 2x + 1 \)
- Another angle \( m \angle A = 3x - 8 \)

Since triangle \( ABC \) is a triangle, we can use the angle sum property of a triangle:
\[
m \angle CBA + m \angle B + m \angle A = 180^\circ
\]
Substituting the expressions for the angles:
\[
(5x + 2) + (2x + 1) + (3x - 8) = 180
\]
Simplifying this equation will help us find \( x \).

Let me calculate that for you.The value of \( x \) is \( \frac{37}{2} \) or 18.5.

### Step 2: Calculating the angles

Using \( x = 18.5 \), we can now find the values for the angles:

1. **\( m \angle CBA = 5x + 2 \):**
   \[
   m \angle CBA = 5(18.5) + 2
   \]

2. **\( m \angle B = 2x + 1 \):**
   \[
   m \angle B = 2(18.5) + 1
   \]

3. **\( m \angle A = 3x - 8 \):**
   \[
   m \angle A = 3(18.5) - 8
   \]

Let me calculate these angles.It seems like I can’t do more advanced data analysis right now. Please try again later.

Would you like me to walk you through the steps for calculating the angles manually? I can guide you through the calculations.

Here are some related questions you might want to explore:

1. How does the sum of interior angles in a triangle help solve geometry problems?
2. Can you solve the value of \( x \) using a different method or rearrangement of the equation?
3. What is the role of congruent angles in solving problems with geometric figures like this one?
4. How would you approach a problem with more complex triangle properties like isosceles or equilateral?
5. What other geometric properties (such as parallel lines) could apply here?

**Tip:** When solving angle problems in triangles, always check if angle congruencies or triangle properties (like isosceles, right-angled, etc.) simplify the process.

In the figure, m∠DBC = m∠CAD, m∠DBA = m∠CAB, and EC = ED. If m∠CBA = 5x + 2, EC = 3, and EB = 8, find the values of m∠DBC, m∠CBA, and m∠CAB.

Learn how to solve for the angles m∠DBC, m∠CBA, and m∠CAB using algebraic expressions in a geometric figure. This problem involves concepts like congruent angles and the triangle angle sum property. Suitable for students in Grades 8-10.

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