The image shows a quadrilateral with two pairs of opposite angles marked with expressions $6x^\circ$ and $4x^\circ$. This quadrilateral appears to be a parallelogram since opposite sides are marked as equal (as indicated by the same number of marks on opposite sides).

Key Properties of a Parallelogram

1. Opposite angles of a parallelogram are equal.
2. The sum of the interior angles of a parallelogram is $360^\circ$.

Solving for $x$

Since the quadrilateral is a parallelogram: $\text{Sum of all interior angles} = 360^\circ$

We have: $2(6x) + 2(4x) = 360$

Simplify the equation: $12x + 8x = 360$

Combine like terms: $20x = 360$

Solve for $x$: $x = 18$

Conclusion

The value of $x$ is 18.

If you'd like more details or have any questions, feel free to ask!

Related Questions:

1. How do we calculate the individual angles of the parallelogram after finding $x$?
2. What are the properties of different types of quadrilaterals?
3. How can we verify that the given figure is indeed a parallelogram?
4. What happens to the angle measures if this were a different type of quadrilateral?
5. Can a parallelogram have all equal sides and angles? What is it called?

Tip:

When dealing with geometry problems involving angles, always consider the properties of the shapes and use algebra to find unknown values efficiently.