Answer:
 The measure of ∠QRS is 58° .
Explanation:
Definition of the bisect 
Bisect means divided anything in two equal parts .
As given 
RS bisects ∠QRT.
This RS divided the ∠QRT into two equal parts .
 If m∠QRT = 116 .
Thus 


∠QRS = 58° 
Therefore the measure of ∠QRS is 58° .