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From the diagram, you are asked to calculate the size of angle \( T_2 \). The diagram contains two intersecting circles, and various geometric markings are shown, including angles around points \( S \), \( T \), \( O \), and \( R \), with given angles and points marked.

### Step-by-Step Approach:

1. **Identify the key relationships**: The angle \( R \) (at the bottom of the diagram) is marked as \( 55^\circ \), and this is an inscribed angle in the circle passing through points \( T \), \( S \), and \( V \). Inscribed angles subtended by the same arc in a circle are equal.
   
2. **Focus on arc \( RV \)**: Angle \( T_2 \) is also subtended by the same arc \( RV \), which means:
   \[
   \angle T_2 = \angle R = 55^\circ
   \]

Thus, the size of angle \( T_2 \) is \( 55^\circ \).

Let me know if you'd like more detailed reasoning or have any other questions!

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### Related questions:
1. What is the rule governing angles subtended by the same arc in a circle?
2. How does the exterior angle theorem apply to circle geometries?
3. Can the angle at the center of a circle be related to inscribed angles?
4. How do intersecting circles affect the angles in the overlapping region?
5. Can the sum of opposite angles in a cyclic quadrilateral give us useful relationships?

### Tip:
When dealing with circle geometry, always look for inscribed angles subtended by the same arc to simplify your calculations.

Calculate the size of angle T_2 from the given geometric diagram of two intersecting circles with labeled angles.

In this circle geometry problem, learn how to calculate the size of angle T_2. The problem involves intersecting circles and uses the theorem that angles subtended by the same arc are equal. This solution is suitable for students in Grades 9-12.

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