MathematicsABCD is a cyclic quadrilateral in which BC||AD. ∠ADC= 110 °   and ∠BAC= 50 °  . Find ∠DAC  .

ABCD is a cyclic quadrilateral in which BC||AD. ADC= 110 °   and BAC= 50 °  . Find DAC  .


  1. A
    85o
  2. B
    75o
  3. C
    70o
  4. D
    60o   

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    Solution:

    It is given that ABCD is a cyclic quadrilateral, BC||AD. ADC= 110 °   and BAC= 50 °  .
    In a cyclic quadrilateral, the opposite angles are supplementary.
    ABC+ADC = 180 ° ABC+ 110 ° = 180 ° ABC = 70 °  
    Since AD||BC, the co-interior angles are supplementary.
    DAB+ABC = 180 ° DAC+ 50 ° + 70 ° = 180 ° DAC = 180 ° 120 °      DAC      = 60 °   Therefore, the correct option is (4).
     
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