In trapezium ABCD with AB∥CD, if ∠A=100∘, then ∠D= __

Question

In trapezium ABCD with

A B ∥ C D

, if

∠ A = 100^{\circ}

, then

∠ D =

___.

Answer:
:

80^{\circ}

In a trapezium, we know that the angles on either side of the base are supplementary.
So, in trapezium ABCD, given

A B ∥ C D

∴ ∠ A + ∠ D = 180^{\circ} \Rightarrow 100^{\circ} + ∠ D = 180^{\circ} \Rightarrow ∠ D = 180^{\circ} - 100^{\circ} ∴ ∠ D = 80^{\circ}

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