Question

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

Answer:

Solution:

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

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Let y and z be 3x and 7x

∠x=∠z   (Alternate angles)

∠x+∠y=180∘ (Angles made on same side of transversal)

Put x = z

∠z+∠y=180°

7x + 3x = 180°

10x = 180°

x =180°/10 = 18°

z = 7 × 18° = 126°

x = z = 126°.