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Railways Sample Paper RRBs Assistant Loco Pilot and Technician CBT STAGE-I Sample Paper-35

  • question_answer
    In the given figure \[AB||CD,\]\[\angle ABE=120{}^\circ ,\]\[\angle DCE=100{}^\circ \]and\[\angle BEC=x{}^\circ ,\]then x is equal to

    A)  \[60{}^\circ \]             

    B)  \[50{}^\circ \]

    C)  \[40{}^\circ \]             

    D)  \[70{}^\circ \]

    Correct Answer: C

    Solution :

    Through E draw GEH\\AB\\CD AB\\GE and BE is the transversal. \[\therefore \]      \[\angle ABE+\angle GEB=180{}^\circ \] \[\Rightarrow \]   \[120{}^\circ +\angle GEB=180{}^\circ \] \[\Rightarrow \]               \[\angle GEB=60{}^\circ \] CD\\EH and CE is the transversal.             \[\therefore \]      \[\angle DCE+\angle CEH=180{}^\circ \]             \[\Rightarrow \]   \[100{}^\circ +\angle CEH=180{}^\circ \]             \[\Rightarrow \]               \[\angle CEH=80{}^\circ \] Now, \[\angle GEB+\angle BEC+\angle CEH=180{}^\circ \] \[\Rightarrow \]               \[60{}^\circ +x+80{}^\circ =180{}^\circ \] \[\therefore \]                              \[x=40{}^\circ \]


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