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9th Class Mathematics Lines and Angles Question Bank Lines and angles

  • question_answer
    In the given figure, \[\angle \mathbf{OAB}=\mathbf{6}{{\mathbf{5}}^{{}^\circ }},\]\[\angle \mathbf{OBA}=\mathbf{4}{{\mathbf{5}}^{{}^\circ }}\] and \[\angle \mathbf{OCD}=\mathbf{10}{{\mathbf{0}}^{{}^\circ }}\]. Then \[\angle \mathbf{ODC}\] =?

    A)  \[{{20}^{{}^\circ }}\]                          

    B)  \[{{10}^{{}^\circ }}\]

    C)  \[{{30}^{{}^\circ }}\]                          

    D)  \[{{25}^{{}^\circ }}\]

    Correct Answer: B

    Solution :

    (b): In \[\Delta OAB\], we have: \[\angle OAB+\angle OBA+\angle AOB={{180}^{{}^\circ }}\] \[\therefore \]\[{{45}^{{}^\circ }}+{{65}^{{}^\circ }}+\angle AOB={{180}^{{}^\circ }}\Rightarrow \angle AOB={{70}^{{}^\circ }}\] \[\therefore \]\[\angle COD=\angle AOB={{70}^{{}^\circ }}\] In \[\Delta OCD\], we have:   \[\angle COD+\angle OCD+\angle ODC={{180}^{{}^\circ }}\] \[{{70}^{{}^\circ }}+{{100}^{{}^\circ }}+\angle ODC={{180}^{{}^\circ }}\Rightarrow \angle ODC={{10}^{{}^\circ }}\]


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