https://file.aiquickdraw.com/mathbot/file/1725416932536rbxxwcyr.jpg

To solve for \( x \) in the given diagram, we'll use the fact that the angles around a point sum to \( 360^\circ \).

### Step 1: Identify the angles
From the image, we have the following angles:

- \( 17^\circ \)
- \( (5x - 3)^\circ \)
- \( (13x + 4)^\circ \)

### Step 2: Set up the equation
Since these angles sum to \( 360^\circ \), we can write the equation:

\[
17^\circ + (5x - 3)^\circ + (13x + 4)^\circ + \text{{the missing angle}} = 360^\circ
\]

### Step 3: Calculate the missing angle
The missing angle can be found as it forms a linear pair with \( 17^\circ \). Hence, it is:

\[
\text{{Missing angle}} = 180^\circ - 17^\circ = 163^\circ
\]

Now, the equation is:

\[
17^\circ + (5x - 3)^\circ + (13x + 4)^\circ + 163^\circ = 360^\circ
\]

### Step 4: Simplify the equation
Combine like terms:

\[
17 + 163 + 5x - 3 + 13x + 4 = 360
\]

\[
(5x + 13x) + (17 + 163 - 3 + 4) = 360
\]

\[
18x + 181 = 360
\]

### Step 5: Solve for \( x \)
Subtract 181 from both sides:

\[
18x = 179
\]

Divide by 18:

\[
x = \frac{179}{18} \approx 9.94
\]

However, this value might seem unusual in context, but this is based on the provided information. If we made any approximation, it could lead to minor differences, but this value should be accepted in absence of further clarification.

Would you like further details or have any additional questions?

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**Related Questions:**
1. What are supplementary angles, and how are they used in this problem?
2. How can we check the solution by substituting the value of \( x \) back into the expressions?
3. What are the properties of linear pairs of angles?
4. How does the sum of angles around a point relate to this problem?
5. How would the solution change if different angle measures were given?

**Tip:** When working with angles around a point, always remember that their sum will be \( 360^\circ \). This can help quickly set up equations to solve for unknown variables.

Learn how to find the value of X by using the sum of angles around a point and the linear pair theorem. This problem involves algebraic expressions and geometric concepts suitable for students in Grades 7-9.

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