In figure, If AB || CD, CD || EF and y : z = 3 : 7, find x.

1.	In figure, If AB \|\| CD, CD \|\| EF and y : z = 3 : 7, find x.
Answer» We are given that AB \|\| CD and CD \|\| EF ∴ ∠CQR = ∠QRF = z …(i) (Alternate angles) and ∠APQ = ∠CQR = x …(ii) (Corresponding angles) From (i) and (ii), we get x = z …(iii) Also ∠CQP + ∠CQR= 180° (Linear pair) ⇒ y + z = 180° But y : z = 3 : 7 ⇒ y = 3k and z = 7k ⇒ 3k + 7k = 180° 10k = 180° k = 18° ∴ y = 3k = 3 × 18° = 54° and z = 7k = 7 × 18° = 126° Hence. x = z = 126° [using (iii)]

Answer»

We are given that AB || CD and CD || EF

∴ ∠CQR = ∠QRF = z …(i)

(Alternate angles)

and ∠APQ = ∠CQR = x …(ii)

(Corresponding angles)

From (i) and (ii), we get

x = z …(iii)

Also ∠CQP + ∠CQR= 180°

(Linear pair)

⇒ y + z = 180°

But y : z = 3 : 7

⇒ y = 3k and z = 7k

⇒ 3k + 7k = 180°

10k = 180°

k = 18°

∴ y = 3k = 3 × 18° = 54°

and z = 7k = 7 × 18° = 126°

Hence. x = z = 126° [using (iii)]

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