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9th Class Mathematics Quadrilaterals Question Bank Quadrilateral

  • question_answer
    In the given figure, ABCD is a square. A line segment DX cuts the side BC at X and the diagonal AC at 0 Such that \[\angle \mathbf{COD}=\mathbf{11}{{\mathbf{5}}^{{}^\circ }}\]and \[\angle \mathbf{OXC}={{\mathbf{x}}^{{}^\circ }}\]. The value of x is:

    A)  \[{{40}^{{}^\circ }}\]                       

    B)  \[{{60}^{{}^\circ }}\]

    C)  \[{{80}^{{}^\circ }}\]                                   

    D)  \[{{85}^{{}^\circ }}\]

    Correct Answer: B

    Solution :

    (b):   \[\angle OCX={{45}^{{}^\circ }}\] \[\angle COD+\angle COX={{180}^{{}^\circ }}\] \[\angle COX={{180}^{{}^\circ }}-\angle COD={{180}^{{}^\circ }}-{{115}^{{}^\circ }}={{65}^{{}^\circ }}\] In \[\Delta OCX\] \[\angle OCX+\angle COX+\angle OXC={{180}^{{}^\circ }}\] \[\Rightarrow \]\[{{45}^{{}^\circ }}+{{65}^{{}^\circ }}+\angle OXC={{180}^{{}^\circ }}\] \[\Rightarrow \]\[\angle OXC={{180}^{{}^\circ }}-{{110}^{{}^\circ }}={{70}^{{}^\circ }}\Rightarrow x={{70}^{{}^\circ }}\]


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