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

  • question_answer
    In the figure, \[\mathbf{AB}\parallel \mathbf{CD}.\]If \[\angle \mathbf{EAB}=\mathbf{4}{{\mathbf{5}}^{{}^\circ }}\]and \[\angle \mathbf{ECD}=\mathbf{5}{{\mathbf{5}}^{{}^\circ }}\], then \[\angle \mathbf{AEB}=\]?

    A)  \[{{50}^{{}^\circ }}\]                                   

    B)  \[{{60}^{{}^\circ }}\]

    C)  \[{{80}^{{}^\circ }}\]     

    D)  \[{{55}^{{}^\circ }}\]

    Correct Answer: C

    Solution :

    (c): Let \[\angle AEB={{x}^{{}^\circ }}\]. Now, \[AB\parallel CD\] and BC is the transversal. \[\therefore \]\[\angle ABE=\angle BCD={{55}^{{}^\circ }}\] In \[\Delta ABE\] we have \[{{45}^{{}^\circ }}+{{55}^{{}^\circ }}+x={{180}^{{}^\circ }}\] \[\Rightarrow \]\[x={{80}^{{}^\circ }}.\]                      


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