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# 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 = $$126^\circ$$