In the diagram, STUV is a straight line. < TSY = < UXY = 40o and < VUW = 110o. Calculate < TYW
150o
140o
130o
120o
Correct answer is A
< TUW = 110o = 180o (< s on a straight line)
< TUW = 180o - 110o = 70o
In \(\bigtriangleup\) XTU, < XUT + < TXU = 180o
i.e. < YTS + 70o = 180
< XTU = 180 - 110o = 70o
Also < YTS + < XTU = 180 (< s on a straight line)
i.e. < YTS + < XTU - 180(< s on straight line)
i.e. < YTS + 70o = 180
< YTS = 180 - 70 = 110o
in \(\bigtriangleup\) SYT + < YST + < YTS = 180o(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) = 360o - 60
2(< TYW) = 300o
TYW = \(\frac{300}{2}\) = 150o
< SYT
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