Find the value of x if l || m || n and y: z = 5: 4.

Given: Line l || Line m || Line n and line t is transversal and y : z = 5 : 4

From the figure, ∠1 = z... (Corresponding Angles as Line m || Line n)
∠y + ∠z = 180°..(Linear Pair)
⇒ 5k + 4k = 180°
⇒ 9k = 180°
⇒ k = 20°
⇒ ∠y = 5k = 100° and ∠z = 4k = 80°.
Now, ∠z = ∠x...(Corresponding Angles as Line l || Line m)
⇒ x = 80°.