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

It is given in the question that:

AB || CD,
Thus,
∠x + ∠y = 180°      ( Interior angles on same side of transversal )  (1)
Also,
AB || CD and CD || EF

Thus, AB || EF
⇒ ∠x = ∠z        ( Alternate interior angles)         (2)
From (1) and (2) we can say that,
∠z + ∠y = 180°           (3) [Angles will be supplementary]
It is given that,
∠y : ∠z = 3 : 7           (4)
Let ∠y = 3 a and ∠z = 7 a
Putting these values in (2)
3 a + 7 a = 180°
10 a = 180°
a = 18°
∠z = 7 a
∠z = 7 x 18°
∠z = 126°
As ∠z = ∠x
∠x = 126°

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