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

  • question_answer
    In the given figure, if \[\mathbf{EC}\parallel \mathbf{AB},\]\[\angle \mathbf{ECD}=\mathbf{6}{{\mathbf{5}}^{{}^\circ }},\] \[\angle \mathbf{BDO}=\mathbf{2}{{\mathbf{5}}^{{}^\circ }}\], then \[\angle \mathbf{OBD}\] is to:

    A)  \[{{40}^{{}^\circ }}\]      

    B)  \[{{65}^{{}^\circ }}\]            

    C)  \[{{115}^{{}^\circ }}\]                                  

    D)  \[{{70}^{{}^\circ }}\]

    Correct Answer: A

    Solution :

    (a): \[\angle AOD=\angle ECO\Rightarrow \angle AOD={{65}^{{}^\circ }}\] So, \[\angle BOD={{115}^{{}^\circ }}\] Hence in \[\Delta BOD\] \[\angle OBD+\angle BOD+\angle ODB={{180}^{{}^\circ }}\] \[\angle OBD={{180}^{{}^\circ }}-\left( {{115}^{{}^\circ }}+{{25}^{{}^\circ }} \right)\] \[\angle OBD={{40}^{{}^\circ }}\]                 


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