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7th Class Mathematics Lines and Angles Question Bank Lines And Angles

  • question_answer
    In the figure (not drawn to scale), ABC and CDE are straight lines, \[\angle ACE\] is a right angle, \[DF||CG||BH\]. Find          \[\angle Y\].

    A)  \[{{65}^{o}}\]                    

    B)  \[{{73}^{o}}\]        

    C)         \[{{62}^{o}}\]        

    D)         \[{{60}^{o}}\]

    Correct Answer: C

    Solution :

    Since, CG||DF and CE is transversal. \[\therefore \] \[\angle GCE=\angle FDE\] (Corresponding angles) \[\Rightarrow \]  \[\angle GCE={{28}^{o}}\] Now, \[\angle ACE={{90}^{o}}\](given) \[\Rightarrow \]  \[\angle ACG+\angle GCE={{90}^{o}}\] \[\angle ACG+{{28}^{o}}={{90}^{o}}\] \[\therefore \] \[\angle ACG={{90}^{o}}-{{28}^{o}}={{62}^{o}}\] Also, \[BH||CG\]and CA is transversal. \[\therefore \]  \[\angle Y=ACG\]       (Corresponding angles) \[\Rightarrow \]  \[\angle Y={{62}^{o}}\]


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