In the figure, point O is the center of the circle, the measure of angle RTB is 28

Call the point  where  BT  intersects the circle, A

And  we have  that

Measure of angle RTB  =  (1/2)  ( measure of minor arc RB - measure of minor arc SA)

But angle SOT  = measure of angle  SOA

And since SOA  is a  central angle, it has  the same measure as minor arc SA

And.....since ROB is also a central angle, it has the same measure as minor arc RB

Call the meaure of  minor arc SA =  angle SOT  = angle SOA  =  M

And call the measure of minor arc RB  = angle ROB =  4M

So  we have this equation

28  = (1/2) (4M - M)

56  = 3M

56/3  =  M

So  ,minor arc  SA = (56/3)°

And minor  arc RB   =  4 (56/3)  = (224/3)°

And  minor arc RS  =   180  - 56/3 - 224/3   = (260/3)° ≈  86.66°

Important: When a tangent and a secant, two secants, or two tangents intersect outside a circle then the measure of the angle formed is one-half the positive difference of the measures of the intercepted arcs.

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∠SOT = xº         ∠ROB = (4x)º            ∠RTB = 28º

 ∠RTB = 1/2 (∠ROB - ∠SOT)     

28º = 1/2 (4x - x)            x = 18.6666666

Arc RS = 180 - 5x = 86.6666666º