https://file.aiquickdraw.com/mathbot/file/1731962551994l2btnrgr.jpg

To solve the problem, we will use the concept of exterior and interior angles in a triangle.

### Step 1: Recall the exterior angle theorem
The exterior angle of a triangle is equal to the sum of the two remote interior angles.

Here:
- The exterior angle is \(150^\circ\),
- One of the interior angles is \(47^\circ\),
- The other interior angle is \(x^\circ\).

Using the formula:
\[
\text{Exterior angle} = \text{Interior angle 1} + \text{Interior angle 2}
\]

Substitute the known values:
\[
150^\circ = 47^\circ + x^\circ
\]

### Step 2: Solve for \(x\)
\[
x^\circ = 150^\circ - 47^\circ
\]
\[
x^\circ = 103^\circ
\]

### Final Answer:
\[
x = 103^\circ
\]

Let me know if you'd like more details or have any further questions!

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### Related Questions:
1. What is the total sum of interior angles in a triangle?
2. How do we identify an exterior angle in a triangle?
3. What happens when two angles in a triangle are equal?
4. Can exterior angles be obtuse or acute, and why?
5. How does this concept apply to real-world problems?

### Tip:
Always double-check the diagram to ensure the angles are labeled correctly before applying formulas.

Find the value of x using the exterior angle theorem for the given triangle diagram.

Learn how to solve for x in a triangle using the exterior angle theorem. The problem involves a 150° exterior angle and a 47° interior angle. A step-by-step solution explains the relationship between exterior and interior angles. Suitable for Grades 6-8.

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