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Question

In the given figure, if ABCD, CDEF and y:z=3:7, find x.

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Solution

It is given that ABCD and CDEF

ABCDEF (Lines parallel to the same line are parallel to each other)

It can be observed that

x=z (Alternate interior angles) … (1)

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

Let the common ratio between y and z be a.

y=3a and z=7a

Also, x+y=180 (Co-interior angles on the same side of the transversal)

z+y=180 [Using equation (1)]

7a+3a=180

10a=180

a=18

Now,

x=7a=7×18=126


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