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To solve for \( x \) in the given right triangle using the triangle sum theorem, we can follow these steps:

### Step 1: Understand the Triangle Sum Theorem
The triangle sum theorem states that the sum of the interior angles of a triangle is always \( 180^\circ \).

### Step 2: Identify the Known Angles
- The right angle in the triangle is \( 90^\circ \).
- Another angle is given as \( 50^\circ \).
- Let \( x \) be the third angle that we need to find.

### Step 3: Apply the Triangle Sum Theorem
According to the triangle sum theorem:
\[
90^\circ + 50^\circ + x = 180^\circ
\]

### Step 4: Solve for \( x \)
\[
x = 180^\circ - (90^\circ + 50^\circ)
\]
\[
x = 180^\circ - 140^\circ = 40^\circ
\]

### Final Answer:
\[
x = 40^\circ
\]

Would you like any further explanation or details on this solution? Here are some related questions for further exploration:

1. What is the relationship between the angles in a right triangle?
2. How can the Pythagorean theorem be applied to find the length of a side in a right triangle?
3. What are complementary angles, and how do they relate to right triangles?
4. How would you solve for the angles in a non-right triangle?
5. What is the significance of special right triangles, like 45°-45°-90° and 30°-60°-90° triangles?

**Tip:** Remember that the sum of the two non-right angles in a right triangle will always be \( 90^\circ \).

Use the triangle sum theorem to solve for x in the right triangle where one angle is 50°.

Learn how to solve for angle x in a right triangle using the triangle sum theorem. This problem involves understanding the sum of the interior angles in a triangle, and applying basic geometry concepts. Suitable for students in Grades 7-8.

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