PQRS is a cyclic quadrilateral. If $$\angle$$P is four times $$\angle$$R and $$\angle$$S is three times $$\angle$$Q, then the sum of $$\angle$$Q and $$\angle$$R is:

As PQRS is a cyclic quadrilateral , and  in a cyclic quadrilateral sum of tow opposite angles is 180 degree,

so ,angle P + angle R = 180 degree--------(1)  and angle S +angle Q = 180 degree------(2)

It is given that angle P is 4 times angle R ( P= 4 R)--------(3)

also, angle S is 3 times angle Q (S=3 Q)--------(4)

so, from (1) and (3) P +R = 180 

                              P+ 4R= 180

                              5R= 180

                              R= 180/5=36 degree.

   from (2) and (4) S + Q= 180

                          3Q + Q=180

                           4Q=180

                          Q=180/4= 45 degree.

So, Q+ R = 36 + 45 = 81 degrees.