The image contains a geometric diagram with two intersecting lines that create several angles. The problem asks to solve for an angle labeled "x" by using the properties of these angles.

Analysis:

1. Identifying the Angles:

   • The lines $AB$ and $CD$ intersect at a point creating vertical angles.
   • There is an exterior angle formed by extending one of the lines.

2. Using Angle Properties:

   • Vertical angles are equal. If two angles are vertical, then their measures are equal.
   • Linear pair of angles: If two angles form a straight line, they are supplementary, meaning their sum is $180^\circ$.

Problem Breakdown:

The diagram shows:

• $\angle x$ which needs to be found.
• Adjacent angles and their relationships (possibly involving complementary or supplementary relationships).

However, since the image isn't fully clear on the exact values or other labels, I would need to clarify any missing details before solving it precisely.

Would you like to describe any particular angle values or relationships in the diagram, or should I attempt a general approach based on typical geometry principles?