MathematicsState true or false.ABCD is a cyclic quadrilateral such that ∠A = 90°, ∠B = 70°, ∠C = 95° and ∠D = 105°.

State true or false.


ABCD is a cyclic quadrilateral such that ∠A = 90°, ∠B = 70°, ∠C = 95° and ∠D = 105°.


  1. A
    True
  2. B
      False 

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    Solution:

    Given that,  ABCD   is a cyclic quadrilateral where, ∠A= 90 ° ,∠B= 70 ° ,∠C= 95 ° ,∠D= 105 ° .   We have the pair of opposite angles in cyclic quadrilateral are:
    ∠A= 90 ° ,∠C= 95 °   and ∠B= 70 ° ,∠D= 105 °   We know that the sum of both pair of opposite angles of a cyclic quadrilateral is 180 °  .
    So, we have the pair of opposite angles is,
    ∠A= 90 ° ,∠C= 95 °   ∠A+∠C= 95 ° + 90 °   ∠A+∠C= 185 °   The pair of angles are greater than 180 °  .
    Thus, ABCD   is not a cyclic quadrilateral and the given statement is false.
    Hence, option 2 is correct.
     
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