In the diagram, STUV is a straight line. < TSY = < UXY = 40o...

Explanation

< TUW = 110^o = 180^o (< s on a straight line)

< TUW = 180^o - 110^o = 70^o

In \(\bigtriangleup\) XTU, < XUT + < TXU = 180^o

i.e. < YTS + 70^o = 180

< XTU = 180 - 110^o = 70^o

Also < YTS + < XTU = 180 (< s on a straight line)

i.e. < YTS + < XTU - 180(< s on straight line)

i.e. < YTS + 70^o = 180

< YTS = 180 - 70 = 110^o

in \(\bigtriangleup\) SYT + < YST + < YTS = 180^o(Sum of interior < s)

SYT + 40 + 110 = 180

< SYT = 180 - 150 = 30

< SYT = < XYW (vertically opposite < s)

Also < SYX = < TYW (vertically opposite < s)

but < SYT + < XYW + < SYX + < TYW = 360

i.e. 30 + 30 + < SYX + TYW = 360

but < SYX = < TYW

60 + 2(< TYW) = 360

2(< TYW) = 360^o - 60

2(< TYW) = 300^o

TYW = \(\frac{300}{2}\) = 150^o
< SYT