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8th Class Mathematics Understanding Quadrilaterals Question Bank Quadrilaterals

  • question_answer
    The opposite angles of a parallelogram are \[{{\left( \mathbf{3x}+\mathbf{5} \right)}^{{}^\circ }}\]and\[{{\left( \mathbf{61}-\mathbf{x} \right)}^{{}^\circ }}\]. Find the measure of four angles.

    A)  \[{{47}^{{}^\circ }},{{133}^{{}^\circ }},{{47}^{{}^\circ }},{{133}^{{}^\circ }}\]

    B)  \[{{80}^{{}^\circ }},{{100}^{{}^\circ }},{{80}^{{}^\circ }},{{100}^{{}^\circ }}\]

    C)  \[{{77}^{{}^\circ }},{{103}^{{}^\circ }},{{77}^{{}^\circ }},{{103}^{{}^\circ }}\]         

    D)  \[{{94}^{{}^\circ }},{{86}^{{}^\circ }},{{94}^{{}^\circ }},{{86}^{{}^\circ }}\]

    Correct Answer: A

    Solution :

    (a): Opposite \[\angle s\] of parallelogram are equal. \[\Rightarrow 3x+5=61-x\] \[\Rightarrow 4x=56=x={{14}^{{}^\circ }}\] \[\Rightarrow 3x+5={{47}^{{}^\circ }}.\] Adjacent \[{{\Delta }^{1e}}={{180}^{{}^\circ }}-{{47}^{{}^\circ }}={{133}^{{}^\circ }}\] \[\Delta \,are\,{{47}^{{}^\circ }},{{133}^{{}^\circ }},{{47}^{{}^\circ }},{{133}^{{}^\circ }}\]    


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