Q. 34.6( 23 Votes )

# In the adjoining figure, is a trapezium in which If and find and

Answer :

Here given that ABCD is trapezium where AB || DC.

We observe that ∠ A and ∠ D are the interior angles on the same side of transversal line AD, whereas ∠ B and ∠ C are the interior angles on the same side of transversal line BC.

As ∠A and ∠D are interior angles, we have,

∠A + ∠D = 180°

∴ ∠D = 180° − ∠A

∴ ∠ D = 180° − 55° = 125°

Similarly for ∠ B and ∠C,

∠ B + ∠C = 180°

∴ ∠C = 180°− ∠B

∴ ∠ C = 180° − 70° = 110°

Hence, measure of ∠ D and ∠ C are 125°and 110° respectively.

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