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8th Class Mathematics Understanding Quadrilaterals Question Bank Understanding Quadrilaterals

  • question_answer
    In the given figure (not drawn to scale), DO and CO are the bisectors of \[\angle ADC\] and \[\angle BCD\]respectively. If \[\angle ADC=\angle BCD=60{}^\circ \] and \[\angle DAB=100{}^\circ \], find the measure of \[\angle DOC\] and \[\angle ABC\]respectively,

    A)  \[100{}^\circ \], \[160{}^\circ \]                

    B) \[\text{110 }\!\!{}^\circ\!\!\text{ }\], \[150{}^\circ \]           

    C)  \[120{}^\circ \], \[140{}^\circ \]    

    D)         \[\text{110 }\!\!{}^\circ\!\!\text{ }\], \[130{}^\circ \]

    Correct Answer: C

    Solution :

    In\[\Delta OCD\], We have \[\angle DOC+\angle ODC+\angle DCO=180{}^\circ \]                                     [Angle sum property] \[\Rightarrow \angle DOC+30{}^\circ +30{}^\circ =180{}^\circ \] \[\angle DOC=180{}^\circ -60{}^\circ =120{}^\circ \] Now, in quadrilateral ABCD, we have \[\angle DAB+\angle ADC+\angle BCD+\angle ABC=360{}^\circ \] \[\Rightarrow 100{}^\circ +60{}^\circ +60{}^\circ +\angle ABC=360{}^\circ \] \[\Rightarrow 220{}^\circ +\angle ABC=360{}^\circ \] \[\Rightarrow \angle ABC=360{}^\circ -220{}^\circ =140{}^\circ \]


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