Q. 24.0( 351 Votes )

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

Answer :

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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