MathematicsState 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 ABDC, A=105°, AD=3cm, AB=4 cm and CD=8cm is 


  1. A
    True
  2. B
    False 

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    Solution:

    Given that in trapezium ABCD, ABDC, A=105°, AD=3cm, AB=4 cm and CD=8cm.
    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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