The image shows a right-angled triangle, and I can see the following key information:

• Angle $\angle ABC = 20^\circ$
• Angle $\angle BDC = 90^\circ$
• Angle $\angle DBC = 65^\circ$

We are required to find the value of $x$, which seems to represent the length of one side of the triangle, though I will clarify by working through the triangle and relations.

Let's summarize the angles first:

1. In triangle $BDC$, the sum of the angles must be $180^\circ$ as it's a triangle: $\angle DBC + \angle BDC + \angle BCD = 180^\circ$ Substituting known angles: $65^\circ + 90^\circ + \angle BCD = 180^\circ$ Solving for $\angle BCD$: $\angle BCD = 180^\circ - 155^\circ = 25^\circ$

2. Using these angle relationships and the geometry of the triangle, we can further explore the sides based on trigonometry. However, more information about the side lengths is necessary to calculate $x$.

Please confirm whether $x$ is the length of one of the sides (for example, $BD$ or $BC$) or provide any other clarifications.

Do you want a step-by-step solution once the side $x$ is confirmed?

Here are five related questions to consider:

1. Is $x$ the length of side $BD$ or another side in the diagram?
2. Would you like to calculate any other side of the triangle, such as $BC$ or $AB$?
3. Should we use trigonometric functions (sine, cosine, etc.) to solve for $x$?
4. Are there additional lengths given for sides not visible in this portion of the problem?
5. Would you like to explore any other properties of the triangles formed?

Tip: Always check for basic geometric relationships such as the sum of angles in a triangle before applying trigonometry!