Q. 24.1( 14 Votes )
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.
Answer :
=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]
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