MathematicsABCD is a cyclic quadrilateral in which ∠BCD= 100 °  and ∠ABD= 70 °  . The measure of ∠ABD   will be ____o.

ABCD is a cyclic quadrilateral in which BCD= 100 °  and ABD= 70 °  . The measure of ABD   will be ____o.


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    Solution:

    ABCD is a cyclic quadrilateral in which BCD= 100 °  and ABD= 70 °  . The measure of ABD   will be 30o.
    It is given that ABCD is a cyclic quadrilateral, BCD= 100 °  and ABD= 70 °  .
    The opposite angles of a cyclic quadrilateral are supplementary.
    A+C= 180 ° B+D= 180 °  
    DAB+DCB = 180 ° DAB+ 100 ° = 180 ° DAB = 80 °         ………. (i)
     In ΔABD  ,
    The sum of angles of a triangle is 180 °  .
    ADB+DAB+ABD = 180 ° 80 ° +ADB+ 70 ° = 180 ° ADB = 30 °                     …From (i)
    Hence, the measure of ABD   will be 30o.
     
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