Question

2. In Fig. 3.29. if AB || CD. CD || EF and y:z=3:7,
find x.​

Answer 1

Answer:

∠y  = 54°

∠z = 126°

∠x = 126°

Step-by-step explanation:

In Fig. 3.29. if AB || CD. CD || EF and y:z=3:7,

find x.​

∠y + ∠z = 180°

y:z=3:7

Let say y = 3k  & z = 7k

3k + 7k =  180°

=> 10k = 180°

=> k = 18

∠y  = 3*18 = 54°

∠z = 7*18 = 126°

∠x = ∠z = 126°

Answer 2

wrong fig.

correct fig is in the attachment please refer to that

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Given AB || CD, CD || EF and y : z = 3 : 7

To find x

Solution

∠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)

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°

From.... (3),

126°+ ∠y = 180°

∠y = 54°