https://file.aiquickdraw.com/mathbot/file/1729721860520pj359mop.jpg

To solve this problem, we need to determine the value of \(x\) based on the given angles in the triangle.

### Step 1: Analyze the Triangle
The triangle has three angles:
- One angle is labeled as \( (3x)^\circ \).
- Another angle is labeled as \( (4x - 10)^\circ \).
- The third angle outside the triangle is a linear pair with one of the angles in the triangle and is \(130^\circ\). Therefore, the interior angle of the triangle adjacent to this is \(180^\circ - 130^\circ = 50^\circ\).

### Step 2: Use the Triangle Angle Sum Theorem
The sum of the interior angles in a triangle is always \(180^\circ\). So, we can write the equation:
\[
3x + (4x - 10) + 50 = 180
\]

### Step 3: Simplify the Equation
Combine like terms:
\[
3x + 4x - 10 + 50 = 180
\]
\[
7x + 40 = 180
\]

### Step 4: Solve for \(x\)
Subtract 40 from both sides:
\[
7x = 140
\]

Divide by 7:
\[
x = 20
\]

The value of \(x\) is 20.

### Answer
The correct answer is:
**A. 20**

Would you like a deeper explanation or have any questions?

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Here are five related questions to further practice:
1. What is the measure of each angle in the triangle?
2. How would the equation change if the exterior angle was \(120^\circ\) instead of \(130^\circ\)?
3. If \(x = 25\), what would the interior angles of the triangle be?
4. How does the triangle angle sum theorem apply to non-Euclidean geometry?
5. How can you determine the type of triangle based on its angle measures?

**Tip:** When solving for angles in a triangle, always remember that the sum of the interior angles equals \(180^\circ\).

What is the value of x in a triangle where one angle is (3x)°, another angle is (4x - 10)°, and the exterior angle adjacent to one of the angles is 130°?

Learn how to solve for the value of x in a triangle with angles (3x)°, (4x - 10)°, and an exterior angle of 130°. This problem uses the Triangle Angle Sum Theorem and the concept of a linear pair. Suitable for Grades 7-10.

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