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

  • question_answer
    In a \[\Delta PQR,\,\,PQ=PR\] and \[\angle Q\] is twice that of \[\angle P\]. What is the measure of \[\angle Q\]?

    A)  \[{{72}^{o}}\]     

    B)         \[{{36}^{o}}\]

    C)  \[{{144}^{o}}\]

    D)         \[{{108}^{o}}\]

    Correct Answer: A

    Solution :

     Since \[PQ=PR,\] \[\angle Q=\angle R\] Given that \[\angle Q=2\,\,\angle P,\] we have                 \[\angle P+\angle Q+\angle R={{180}^{o}}\] \[\Rightarrow \] \[\frac{\angle Q}{2}+\angle Q+\angle Q={{180}^{o}}\] \[\Rightarrow \] \[\frac{5}{2}\,\,\angle Q={{180}^{o}}\,\,\Rightarrow \,\,\angle Q={{72}^{o}}\]


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