This problem involves calculating the unknown angle in a triangle. The given angles are $137^\circ$ and $102^\circ$. Since the sum of the angles in any triangle is always $180^\circ$, the unknown angle can be found as follows:

$\text{Unknown angle} = 180^\circ - (\text{sum of the other two angles})$

$\text{Unknown angle} = 180^\circ - (137^\circ + 102^\circ)$

$\text{Unknown angle} = 180^\circ - 239^\circ$

Since the total exceeds $180^\circ$, this is not a triangle, but likely part of a larger geometric configuration (e.g., exterior angles). Would you like me to analyze this geometry further or clarify? Let me know if you'd like a detailed breakdown!

Follow-Up Questions:

1. How are the angles $137^\circ$ and $102^\circ$ positioned geometrically in this problem?
2. Could this be part of a polygon, rather than a triangle?
3. What additional information (e.g., labeled diagram) can we use to understand this problem?
4. Do you want me to verify the properties of triangles or angles for future reference?
5. Would you like an explanation about exterior angles and their properties?

Tip: Always double-check the geometric configuration to ensure accurate identification of shapes and properties.