Different confusing problems lol

First one

Angle  DEF = 6x + 37

And twice the angle measure of angle DEF =  measure of arc FGD

So...we have that

2(6x + 37)   =  (19x - 31)    simplify

12x + 74 = 19x - 31     rearrange as

74 + 31 =  7x

105 = 7x      

15 = x

So   DEF = 6(15) + 37 =    90 + 37 =    127°

Second one

mSTU = 13x - 6

So....  2*STU = arc SU...so we have

2(13x - 6) = (21x + 8)   simplify

26x   - 12  =  21x + 8

5x = 20

x = 4

So  arc SU =   21(4) + 8 =  92

So

arc SU + arc UT + arc ST = 360

92 + 143 +  arc ST = 360

235 + arc ST = 360

arc ST  = 360 - 235  =  125°