In cyclic quadrilateral PQRS,

P  and R  are  opposite angles in the quadrilateral  such that

P  = (3/5)R           so R > P

So

P  + R  = 180

(3/5)R + R  = 180

(8/5)R = 180

R = 180 * 5/8  =   112.5°

And Q =  (4/5)R = (4/5) (112.5)  =   90°

So  S  must also   = 90°   since Q and S are supplemental

So  R  is the largest angle

Let P=3x,Q=4x,R=5x. Then, the sum of the angles in quadrilateral PQRS is [3x + 4x + 5x + 6x = 180^\circ,]so x=30∘. The largest angle is ∠R=5⋅30∘=150∘​.