https://file.aiquickdraw.com/mathbot/file/1727356817971romxva6v.jpg

The diagram shows a triangle with several given angles. To solve for \( X \), we need to use angle properties of triangles.

### Step 1: Analyze the big triangle
In the large triangle, one angle is given as \( 120^\circ \) (marked in purple). The triangle is split into two smaller triangles by two lines, and these triangles each have one of the angles marked as \( 3X^\circ \) and \( 2X^\circ \).

### Step 2: Use the fact that the sum of angles in any triangle is \( 180^\circ \)

In the smaller right triangle on the right side, the angles are \( 2X^\circ \) and \( X^\circ \), and the third angle (external to this triangle) is part of the overall triangle structure. We need to calculate it by setting up equations based on angle sums and properties.

### Step 3: Solve for \( X \)
We will set up a relationship between \( X \), \( 3X \), and other known angle properties. I'll proceed to solve this.The value of \( X \) is \( 10^\circ \).

Would you like a more detailed explanation, or do you have any questions?

Here are 5 related questions to expand your understanding:
1. How do we apply the sum of angles in a triangle in different types of problems?
2. What is the role of external angles in geometry?
3. Can you identify different types of triangles based on their angles?
4. How do angle bisectors affect the properties of a triangle?
5. How do supplementary angles help in solving triangle-related problems?

**Tip:** Always remember that the sum of interior angles in any triangle is \( 180^\circ \), and this property can be very helpful in solving geometric problems.

Solve for X in a triangle where one angle is 120 degrees, and two smaller angles are 3X and 2X degrees respectively.

This problem involves solving for X in a triangle where one angle is 120 degrees, and two angles are given as 3X and 2X. The solution involves using the angle sum property of triangles, basic algebra, and angle relationships. Suitable for students in Grades 7-10.

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