1. **Problem statement:** We are given a circle with points R, T, S on its circumference and a tangent line PQ⃗ touching the circle at point R. 2. The angle between the tangent line at R and the chord RS is given as 72°. 3. **Key theorem:** The angle between a tangent and a chord through the point of tangency equals the measure of the intercepted arc divided by 2. Mathematically, if $\angle \text{tangent-chord} = \theta$, then the intercepted arc measure $m = 2\theta$. 4. Here, the tangent-chord angle is $72^\circ$, so the intercepted arc RS has measure: $$m_{RS} = 2 \times 72^\circ = 144^\circ$$ 5. The circle's total circumference is $360^\circ$. The arc RTS is the major arc that includes points R, T, and S, so it is the larger arc opposite to RS. 6. Therefore, the measure of the major arc RTS is: $$m_{RTS} = 360^\circ - m_{RS} = 360^\circ - 144^\circ = 216^\circ$$ 7. **Final answer:** $$\boxed{216^\circ}$$