To solve for the missing angle $m \angle T$ in the triangle $RST$, let's follow these steps:

1. Identify the Given Information:

   • We have triangle $RST$ where $\angle R = 55^\circ$ and $\angle S = 65^\circ$.
   • According to the third angle theorem, the sum of the angles in a triangle is always $180^\circ$.

2. Set Up the Equation: $\angle R + \angle S + \angle T = 180^\circ$ Substituting the known angles: $55^\circ + 65^\circ + \angle T = 180^\circ$

3. Solve for $\angle T$: $120^\circ + \angle T = 180^\circ$ $\angle T = 180^\circ - 120^\circ$ $\angle T = 60^\circ$

4. Conclusion: The measure of the missing angle $m \angle T$ is $60^\circ$.

Would you like a deeper explanation or have any other questions?

Further Questions to Explore:

1. What is the third angle theorem, and why does it work?
2. How would you solve for missing angles in a triangle with a variable expression?
3. Can you calculate angles in polygons with more than three sides using similar methods?
4. What are some practical applications of the third angle theorem?
5. How does this theorem apply to non-Euclidean geometries?

Tip:

In any triangle, knowing two angles is enough to find the third using the third angle theorem. This is a fundamental property that makes triangles unique in geometry.