State whether the following statement is true or false.The diagram of a trapezium ABCD in which AB∥DC, ∠A=105°, AD=3cm, AB=4 cm and CD=8cm is

# State whether the following statement is true or false.The diagram of a trapezium ABCD in which is

1. A
True
2. B
False

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### Solution:

Given that in trapezium ABCD, .
Since, the sum of the adjacent angle of a trapezium is 180°.
Then,
∠A + ∠D = 180°
$⇒$105°+ ∠D = 180°
$⇒$∠D = 180° - 105°
$⇒$∠D = 75°
Draw AB = 4 cm.
Draw AX such that ∠BAX = 105° and mark a point D on AX such that AD = 3 cm.
Draw DY such that ∠ADY = 75° and mark point C such that CD = 8 cm. Join BC.
Therefore, the given figure is correct.
Hence, option (1) is correct.

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