This is a parallelogram, as indicated by the pairs of opposite sides being marked parallel.

In a parallelogram:

1. Opposite angles are equal.
2. Adjacent angles are supplementary (sum up to 180°).

Let's solve for $x$:

1. Set up the equation using the property of supplementary angles: $(x + 35^\circ) + (2x - 15^\circ) = 180^\circ$

2. Combine like terms: $x + 2x + 35^\circ - 15^\circ = 180^\circ$ $3x + 20^\circ = 180^\circ$

3. Solve for $x$: $3x = 180^\circ - 20^\circ$ $3x = 160^\circ$ $x = \frac{160^\circ}{3}$ $x = 53.33^\circ$

So, $x = 53.33^\circ$.

Would you like more details on any step or further explanations?

Here are 5 related questions you might find interesting:

1. How do you prove that opposite angles of a parallelogram are equal?
2. What are the properties of the diagonals in a parallelogram?
3. How do you find the area of a parallelogram given its base and height?
4. How can you determine the angles of a parallelogram if given two adjacent angles?
5. What are the conditions for a quadrilateral to be a parallelogram?

Tip: Always remember, in any polygon, the sum of the exterior angles is always 360°.