In figure, if AB || CD, CD || EF and y : z = 3:7 , find x.

It is given that, y : z = 3:7



Let, y = 3k and z = 7k,

x = \(\angle{CHG}\) (Corresponding angles) ....(i)
Z = \(\angle{CHG}\) (Alternate angles) ....(ii)

From (i) and (ii), we get,
\(\therefore \) x = z ....(iii)
Now, x + y = \(180^\circ\) ....(Internal angles on the same side of the transversal)
From eq.(iii),
z + y = \(180^\circ\)
\(\Rightarrow \) 3k + 7k = \(180^\circ\)
\(\Rightarrow \) 10k = \(180^\circ\)
\(\Rightarrow \) k = \(18^\circ\)

\(\therefore \) y = 3 × \(18^\circ\) and z = 7 × \(18^\circ\)
\(\therefore \) y = \(54^\circ\) and z = \(126^\circ\)
Hence, x = \(126^\circ\)