To find the angle \( f \), let's analyze the properties of the circle and the given angles.

### Observations:

1. **Tangents and Alternate Segment Theorem:**
   - \( RQ \) and \( TP \) are tangents to the circle at points \( R \) and \( T \), respectively.
   - By the tangent-secant theorem, the angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment.

2. **Given Angles:**
   - \( \angle TRP = 105^\circ \)
   - \( \angle RST = e = 105^\circ \)

3. **Circle and Inscribed Angles:**
   - \( \angle SRT = f \)
   - Since \( \angle SRT \) and \( \angle STQ \) are in the same segment subtended by the chord \( RT \), they are equal. 
   - Therefore, \( \angle SRT = \angle STQ = f \).

### Step-by-Step Solution:

1. **Using the Property of a Cyclic Quadrilateral:**
   - In any circle, the sum of opposite angles of a cyclic quadrilateral is \( 180^\circ \).
   - Here, the quadrilateral \( SRTQ \) is cyclic.
   - Thus, \( \angle SRT + \angle STQ = 180^\circ \).

2. **Find Angle \( f \):**
   - We know \( \angle TRP = 105^\circ \), and it's an exterior angle for the triangle \( SRT \).
   - Therefore:
   \[
   \angle SRT + \angle STR = 105^\circ.
   \]

3. **Calculate \( f \):**
   - From the above, \( f + f = 75^\circ \).
   \[
   2f = 75^\circ \implies f = 37.5^\circ.
   \]

### Conclusion:
The value of angle \( f \) is \( \boxed{37.5^\circ} \).

Discover how to find angle f in a cyclic quadrilateral problem solution. Detailed step-by-step analysis using circle geometry and the properties of cyclic quadrilaterals. Suitable for high school students.

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