The image depicts a composite triangle configuration, where some angles are labeled, and we are tasked with finding the value of $X$.

Given details:

• There's a triangle where one of the angles is $120^\circ$.
• Inside this triangle, there are two smaller angles labeled $3X^\circ$ and $2X^\circ$.
• Additionally, there are isosceles triangles indicated by the markings on the sides (with two sides being equal for the smaller triangles).

Steps to Solve:

1. Main Triangle: In the large triangle, one of the angles is $120^\circ$, and the two remaining angles are in the smaller triangles:

   • $3X^\circ$ and $2X^\circ$.

   Since the sum of angles in a triangle is always $180^\circ$, we can form the following equation: $120^\circ + 3X^\circ + 2X^\circ = 180^\circ$

   Simplifying this: $120^\circ + 5X^\circ = 180^\circ$ $5X^\circ = 60^\circ$ $X = 12^\circ$

Thus, the value of $X$ is $12^\circ$.

Let me know if you want further clarification or additional details!

Here are 5 related questions for practice:

1. How would the solution change if the $120^\circ$ angle was different?
2. What are the properties of isosceles triangles that help in problems like these?
3. What is the sum of internal angles in any triangle?
4. Can you solve for the angles in any triangle if only two angles are given?
5. What are the applications of triangle properties in real-world contexts?

Tip: When solving for unknown angles in any triangle, remember that the sum of interior angles always adds up to 180°.