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Solve the value of x in this non-cyclic quadrilateral ?

To solve for the value of \( x \) in this quadrilateral, we need to apply some geometric principles, particularly the sum of angles in a triangle and the sum of the interior angles of the quadrilateral.

### Step-by-step breakdown:

1. **Identify triangles**:
   - There are two triangles inside the quadrilateral: 
     - The triangle on the left contains angles \( 60^\circ \), \( 20^\circ \), and an unknown angle, which I will call \( A \).
     - The triangle on the right contains angles \( 40^\circ \), \( 50^\circ \), and \( x^\circ \).

2. **Calculate the unknown angles in each triangle**:
   - For the triangle on the left:
     \[
     A = 180^\circ - (60^\circ + 20^\circ) = 180^\circ - 80^\circ = 100^\circ
     \]
   - For the triangle on the right:
     Using the same principle (sum of angles in a triangle is 180°):
     \[
     x = 180^\circ - (50^\circ + 40^\circ) = 180^\circ - 90^\circ = 90^\circ
     \]

Thus, the value of \( x \) is \( \boxed{90^\circ} \).

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

### Related Questions:
1. How can we calculate the total interior angle sum of a quadrilateral?
2. Why do the interior angles of a triangle sum to 180°?
3. How do we solve for unknown angles in a cyclic quadrilateral?
4. Can a quadrilateral have all its interior angles being right angles?
5. What are the conditions under which two triangles formed inside a quadrilateral share the same angle?

**Tip:** In any polygon, the sum of the interior angles can be found using the formula \( 180^\circ \times (n-2) \), where \( n \) is the number of sides.

Solve the value of x in this non-cyclic quadrilateral?

Learn how to find the value of x in a non-cyclic quadrilateral with a step-by-step breakdown. This problem involves geometry concepts such as the angle sum properties of triangles and quadrilaterals. Suitable for students in Grades 8-10.

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