https://file.aiquickdraw.com/mathbot/file/17273460048562a074hb4.jpg

To solve for \( \angle x \) in the given parallelogram, let's analyze the figure.

### Step-by-Step Breakdown:

1. **Parallelogram Properties**:
   - In a parallelogram, opposite angles are equal. Hence:
     \[
     \angle A = \angle C \quad \text{and} \quad \angle B = \angle D.
     \]
   
2. **Triangle \( AOD \)**:
   - In triangle \( AOD \), the angles are:
     \[
     \angle AOD = 40^\circ, \quad \angle DAO = 30^\circ, \quad \text{and} \quad \angle ODA = x.
     \]
   - The sum of the angles in any triangle is \( 180^\circ \). Therefore:
     \[
     \angle AOD + \angle DAO + \angle ODA = 180^\circ.
     \]
     Substituting the values:
     \[
     40^\circ + 30^\circ + x = 180^\circ.
     \]
   - Solving for \( x \):
     \[
     x = 180^\circ - 70^\circ = 110^\circ.
     \]

Thus, \( \angle x = 110^\circ \).

Let me know if you'd like more details or have any questions!

### Related Questions:
1. How can you use the properties of parallelograms to find unknown angles in general?
2. Why is the sum of the angles in a triangle always \( 180^\circ \)?
3. What is the significance of diagonals in a parallelogram intersecting at a point?
4. Can the method used here be applied to quadrilaterals other than parallelograms?
5. How do supplementary angles work in relation to parallelograms?

### Tip:
Always remember that the diagonals of a parallelogram bisect each other, which can help in solving many geometry problems involving parallelograms.

In the figure below ABCD is a parallelogram. AC and BD are diagonals meeting at O. Find ∠x.

Learn how to find the unknown angle x in a parallelogram ABCD with diagonals AC and BD intersecting at O. This solution uses the angle sum property of triangles and properties of parallelograms, making it suitable for Grades 9-10 students.

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