In the image, you're asked to solve for $x$ in a trapezoid with some given angles: 108°, 121°, and 59°.

To solve for $x$, we can use the fact that the sum of the interior angles of any quadrilateral is 360°.

Step-by-step solution:

1. The sum of the four angles in the trapezoid must equal 360°: $\text{Angle 1} + \text{Angle 2} + \text{Angle 3} + \text{Angle 4} = 360^\circ$
2. You are given three angles: 108°, 121°, and 59°.

So, we can substitute: $108^\circ + 121^\circ + 59^\circ + x = 360^\circ$ 3. Simplify the equation: $288^\circ + x = 360^\circ$ 4. Solve for $x$: $x = 360^\circ - 288^\circ = 72^\circ$

Thus, $x = 72^\circ$.

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

Here are 5 follow-up questions that expand on this concept:

1. What are the properties of the angles in a trapezoid?
2. How can you find the missing angle in different types of quadrilaterals?
3. What other types of problems use the sum of angles in polygons?
4. How do you approach solving for unknowns in geometry problems?
5. Can a trapezoid have all angles equal?

Tip: Always remember that the sum of the interior angles of a quadrilateral is always 360°.