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To find the value of \( x \) in the triangle, we can use the fact that the sum of the interior angles of any triangle is always \( 180^\circ \).

Given:
- One angle is \( 61^\circ \),
- Another angle is \( 41^\circ \),
- The third angle is \( x^\circ \).

We can set up the equation:
\[
x + 61^\circ + 41^\circ = 180^\circ
\]

Simplifying:
\[
x + 102^\circ = 180^\circ
\]

Now, solve for \( x \):
\[
x = 180^\circ - 102^\circ = 78^\circ
\]

Thus, the value of \( x \) is \( 78^\circ \).

Would you like more details or have any questions? Here are some related questions you could explore:

1. How do you calculate the sum of angles in a polygon?
2. What is the exterior angle theorem in triangles?
3. How does the Pythagorean theorem apply in right triangles?
4. How would this change if the triangle were not a standard triangle but an isosceles one?
5. Can you prove that the sum of the interior angles of any triangle is always 180°?

**Tip:** Always double-check the sum of angles when solving triangle problems to ensure they add up to 180°.

What is the value of x in a triangle where the given angles are 61° and 41°?

Learn how to find the missing angle in a triangle where two angles are given as 61° and 41°. The step-by-step solution uses the angle sum theorem, making it suitable for students in Grades 6-8.

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