Question

In Fig. 8.133, if l1 || l2 and l3 || l4, what is y in the terms of x?
A. 90 + x
B. 90 + 2x
C. 90 -
D. 90 – 2x

Answer 1

y = 90 - x/2

Step-by-step explanation:

l₁ || l₂     l₃ || l₄

y° + y° = 2y°

x° = 180° - 2y°

=> 2y° = 180° - x°

=> y° = 90° - (x/2)°

=> y = 90 - x/2

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Answer 2

Relation between y and x is $\mathbf{y =90 -\frac{x}{2}}$  

Step-by-step explanation:

• Here it is given that  $\mathbf{l_{3}\parallel l_{4}}$

        So

        ∠DEB =∠ACB     (Because corresponding angle are equal)

        ∠DEB  = x      ...1)

• By using linear pair angle for line DF

        ∠FGH + ∠HGD =180°

        2y +∠HGD =180°

        So

        ∠HGD =180° -2y      ...2)

• Here it is also given that  $\mathbf{l_{1}\parallel l_{2}}$

       ∠BED =∠HGD  (Because corresponding angle are equal)

        x = 180° -2y

        2y = 180° -x

        So

        $\mathbf{y =90 -\frac{x}{2}=}$     This is required relation between y and x