# 2. In Fig. 6.29, if AB $||$ CD, CD $||$ EF and y : z = 3 : 7, find x.

Given AB || CD and CD || EF and $y:z = 3:7 \Rightarrow z = \frac{7}{3}y$
therefore, AB || EF and $x =z$ (alternate interior angles)..............(i)

Again, CD || AB
$\\\Rightarrow x+y =180^0\\ \Rightarrow z+y =180^0$.............(ii)

Put the value of $z$ in equation (ii), we get

$\frac{10}{3}y =180^0 \Rightarrow y =54^0$
Then $z=180^0-54^0=126^0$

By equation (i), we get the value of $x=126^0$

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