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9th Class Mathematics Quadrilaterals Question Bank Quadrilaterals

  • question_answer
    If angles \[P,\,\,Q,\,\,R\] and \[S\] of the quadrilateral\[PQRS\], taken in order, are in the ratio\[3:7:6:4\], what is\[PQRS\]?

    A)  A rhombus       

    B)         A parallelogram

    C)                     A trapezium     

    D)         A kite              

    Correct Answer: C

    Solution :

    Let the angles be \[3x,7x,6x\]and \[4x.\] \[\therefore \]\[3x+7x+6x+4x={{360}^{o}}\]or \[20x={{360}^{o}}\]or \[x={{18}^{o}}.\]The angles are \[{{54}^{o}},{{126}^{o}},{{108}^{o}},{{72}^{o}}.\]We see that adjacent angles are supplementary but opposite angles are not equal. Clearly it is a trapezium.


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