< 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