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)]