Question

in fig 6.29 , if AB|| CD, CD || EF and y :z= 3:7, find x
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Answer 1

Step-by-step explanation:

Given that y : z = 3 : 7

Let       ∠ y      = 3a

Then   ∠z       = 7a

∠x and ∠z are alternate interior angles of parallel lines so that

∠x = ∠z                      …(1)

Sum of interior angle on the same side of the transversal is always = 180°

So that

x + y = 180°

plug the value of x from equation (1)

z + y = 180°

plug the value of z and y we get

7a + 3a = 180°

10 a    = 180°

a          = 180°/10

a          = 18

y          = 3a    = 3x18            = 54°

z          = 7a    = 7x18            = 126°

x          = z       = 126°

Answer 2

Step-by-step explanation:

It is known that AB CD and CDEF

As the angles on the same side of a transversal line sums up to 180°,

x + y = 180° —–(i)

Also,

O = z (Since they are corresponding angles)

and, y +O = 180° (Since they are a linear pair)

So, y+z = 180°

Now, let y = 3w and hence, z = 7w (As y : z = 3 : 7)

∴ 3w+7w = 180°

Or, 10 w = 180°

So, w = 18°

Now, y = 3×18° = 54°

and, z = 7×18° = 126°

Now, angle x can be calculated from equation (i)

x+y = 180°

Or, x+54° = 180°

∴ x = 126°