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To solve for \( x \) in this triangle problem, we can use the fact that the sum of the interior angles of a triangle is always \( 180^\circ \).

Given angles:
- One angle is \( 65^\circ \),
- Another angle is \( 73^\circ \),
- The third angle is \( x \).

### Solution Steps
1. Set up the equation for the sum of the angles:
   \[
   65^\circ + 73^\circ + x = 180^\circ
   \]

2. Combine the known angles:
   \[
   138^\circ + x = 180^\circ
   \]

3. Solve for \( x \) by subtracting \( 138^\circ \) from both sides:
   \[
   x = 180^\circ - 138^\circ
   \]
   \[
   x = 42^\circ
   \]

### Answer
The value of \( x \) is \( 42^\circ \).

Would you like a detailed explanation of any of these steps, or do you have further questions?

Here are five related questions for practice:
1. What is the measure of the third angle if two angles in a triangle are \( 50^\circ \) and \( 60^\circ \)?
2. If a triangle has angles \( 30^\circ \) and \( 45^\circ \), what is the measure of the third angle?
3. Can a triangle have two angles of \( 90^\circ \)? Why or why not?
4. If the angles in a triangle are \( x \), \( x + 20^\circ \), and \( 2x \), how can you find the value of \( x \)?
5. What are the properties of an equilateral triangle in terms of angle measures?

**Tip:** Remember, the sum of the angles in any triangle is always \( 180^\circ \), which can help you solve similar problems quickly.

The measures of the angles of a triangle are shown in the figure below. Solve for x. Given angles: 65°, 73°, and x.

Learn how to find the missing angle in a triangle with angles 65° and 73°. This problem uses the Triangle Angle Sum Theorem, providing a clear step-by-step solution suitable for Grades 6-8.

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