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7th Class Mathematics The Triangle and its Properties Question Bank Triangles

  • question_answer
    In  \[\Delta ABC,\]  \[AB=AC,\]  \[\angle A={{40}^{o}}\] ,O is a point inside \[\Delta ABC\] such that \[\angle OBC=\angle OCA\]. Find the measure of \[\angle BOC\].

    A)                  \[{{110}^{o}}\]  

    B)                         \[{{35}^{o}}\]

    C)                  \[{{140}^{o}}\]

    D)         \[{{155}^{o}}\]

    Correct Answer: A

    Solution :

     Given, AB = AC \[\Rightarrow \]   \[\angle ABC=\angle ACB\] Also   \[\angle OBC=\angle OCA\] \[\Rightarrow \]OB and OC are angular bisectors                 \[\therefore \]   \[\angle BOC={{90}^{o}}+\frac{\angle A}{2}\]                                 \[={{90}^{o}}+\frac{{{40}^{o}}}{2}={{90}^{o}}+{{20}^{o}}={{110}^{o}}\]


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