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 $90^\circ$.