In the adjoining figure, AB ||CD are cut by a transversal t at E and F respectively. If =5:4, Find measure of each of the remaining marked angles.

=100°, =80°, =100°=80°, =100°, =80°, =100°, =80°

Given AB ||CD are cut by a transversal t at E and F respectively.

And = 5:4

Let ∠1 = 5a and ∠2 = 4a

∠1 + ∠2 = 180° [Because AB is a straight line]

⇒ 5a + 4a = 180°

⇒ 9a = 180°

⇒ a = 20°

Therefore, ∠1 = 5a

∠1 = 5 × 20° = 100°

∠2 = 4a

∠2 = 4 × 20° = 80°

∠3 = ∠1 = 100° [Opposite angles]

∠4 = ∠2 = 80° [Opposite angles]

∠5 = ∠1 = 100° [Crossponding angles]

∠6 = ∠4 = 80° [Crossponding angles]

∠7 = ∠5 = 100° [Opposite angles]

∠8 = ∠6 = 80° [Opposite angles]