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

  • question_answer
    In a triangle ABC, \[\angle \,A+\frac{1}{2}\angle B+\angle \,C=140{}^\circ \] then \[\angle \,B\] is [SSC CGL Tier II, 2014]

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

    B) \[80{}^\circ \]

    C) \[40{}^\circ \]

    D) \[60{}^\circ \]

    Correct Answer: B

    Solution :

    [b] in \[\Delta \,ABC,\]             \[\angle \,A+\frac{1}{2}\angle \,B+\angle \,C=140{}^\circ \]        …(i) [given] But in \[\Delta \,ABC\]     \[\Delta \,A+\angle \,B+\angle \,C=180\]  …(i) Subtract Eq. (i) from Eq. (ii), we get \[\frac{1}{2}\angle B=40\]\[\Rightarrow \]\[\angle \,B=40\times =80{}^\circ \]


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