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In this problem, we are dealing with a triangle where the goal is to find the value of \( x \).

### Step 1: Understand the setup.
We are given:
- An exterior angle \( \angle FCB = 124^\circ \),
- An interior angle \( \angle ABD = 6x \),
- Another interior angle \( \angle DAC = 2x \).

### Step 2: Use the exterior angle theorem.
The exterior angle theorem states that the exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles.

Here, \( \angle FCB \) is the exterior angle, and its value is given as 124°. The two non-adjacent interior angles are \( \angle ABD \) and \( \angle DAC \).

Thus, we can write the equation:
\[
\angle FCB = \angle ABD + \angle DAC
\]
\[
124^\circ = 6x + 2x
\]
\[
124^\circ = 8x
\]

### Step 3: Solve for \( x \).
To find \( x \), divide both sides by 8:
\[
x = \frac{124^\circ}{8}
\]
\[
x = 15.5^\circ
\]

### Final Answer:
\[
x = 15.5^\circ
\]

Would you like more details or further clarification on any part of this solution?

Here are some related questions:
1. What is the exterior angle theorem?
2. Can you explain why the sum of interior angles of a triangle is always 180°?
3. How would the solution change if the angles were given differently?
4. What happens if the angles are in radians instead of degrees?
5. How does the exterior angle relate to the interior angles in any polygon?

**Tip:** The exterior angle theorem is a handy tool for solving many triangle problems, especially when dealing with angles outside the triangle.

Find the value of x in the geometric diagram where \( \angle FCB = 124^\circ \), \( \angle ABD = 6x \), and \( \angle DAC = 2x \).

Learn how to find the value of x in a triangle using the exterior angle theorem, where the exterior angle is 124 degrees, and the interior angles are 6x and 2x. Suitable for students in Grades 9-11.

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