Question

2. In Fig. 6.29, if AB || CD, CD || EF and y: Z=3:7, find x. fig. 6.29​

Answer 1

Question

$\sf \: In \: Fig. 6.29, if \: AB || CD, CD || EF \: and \: y : z = 3 : 7, find \: x.$

Solution:

$\sf \: Given, y : z = 3 : 7 \\ \sf \: Let ∠ y = 3a\\ \sf \:Then ∠z = 7b\\ \sf \:∠x \: and \: ∠z \: are \: alternate \: interior \: angles \: of \: parallel \: lines \: so \: that\\ \sf \:∠x = ∠z \: \: \: \: \: \: \: \: \: \: \: →①\\ \sf \:Sum \: of \: interior \: angle \: on \: the \: same \: side = 180°\\ \sf \:x + y = 180°\\ \sf \:putting \: value \: of \: x \: from \: equation ①\\ \sf \:z + y = 180°\\ \sf \:putting \: the \: value \: of \: z \: and \: y \\ \sf \:7a + 3a = 180°\\ \sf \:10 a = 180°a = \frac{180}{10} \\ \sf \:a = 18 \\ \\ \sf \:y = 3a \: \: \: = 3x18 \: \: \: \: \: = 54°\\ \sf \:z = 7a \: \: \: = 7x18 \: \: \: \: \: \: = 126°\\ \sf \:x = z = 126°$

$\bold \red{Celestial} \bold{Centrix}$

Answer 2

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°

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