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SSC Quantitative Aptitude Geometry Question Bank Triangles and Their Properties (II)

  • question_answer
    The sides BC, CA and AB of \[\Delta ABC,\] have been produced to D, E and F respectively as shown in the figure, forming exterior angles \[\angle ACD,\]\[\angle BAD\]and\[\angle CBF\] Then,\[\angle ACD+\angle BAE+\angle CBF\] is equal to

    A) \[240{}^\circ \]

    B) \[300{}^\circ \]

    C) \[320{}^\circ \]

    D) \[360{}^\circ \]

    Correct Answer: D

    Solution :

    [d] Clearly, \[\angle 1+\angle BAE=180{}^\circ \] \[\angle 2+\angle CBF=180{}^\circ \] \[\angle 3+\angle ACD=180{}^\circ \,(\angle 1+\angle 2+\angle 3)\] \[+\,(\angle BAC+\angle CBF+\angle ACD)=540{}^\circ \] \[\Rightarrow \]\[180{}^\circ +(\angle BAE+\angle CBF+\angle ACD)\] \[=540{}^\circ \] \[\Rightarrow \]   \[\angle ACD+\angle BAE+\angle CBF=360{}^\circ \]


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