11th Class Mathematics Other Series Question Bank Critical Thinking

  • question_answer If the angles of a quadrilateral are in A.P. whose common difference is\[{{10}^{o}}\], then the angles of the quadrilateral are

    A) \[{{65}^{o}},\,{{85}^{o}},\,{{95}^{o}},\,{{105}^{o}}\]

    B) \[{{75}^{o}},\,{{85}^{o}},\,{{95}^{o}},\,{{105}^{o}}\]

    C) \[{{65}^{o}},\,{{75}^{o}},\,{{85}^{o}},\,{{95}^{o}}\]

    D) \[{{65}^{o}},\,{{95}^{o}},\,{{105}^{o}},\,{{115}^{o}}\]

    Correct Answer: B

    Solution :

    Suppose that\[\angle A={{x}^{0}}\], then\[\angle B=x+{{10}^{o}}\], \[\angle C=x+{{20}^{o}}\]and\[\angle D=x+{{30}^{o}}\] So, we know that \[\angle A+\angle B+\angle C+\angle D=2\pi \] Putting these values, we get \[({{x}^{o}})+({{x}^{o}}+{{10}^{o}})+({{x}^{o}}+{{20}^{o}})+({{x}^{o}}+{{30}^{o}})={{360}^{o}}\] \[\Rightarrow x={{75}^{o}}\] Hence the angles of the quadrilateral are\[{{75}^{o}},\ {{85}^{o}},\ {{95}^{o}},\ {{105}^{o}}\]. Trick: In these type of questions, students should satisfy the conditions through options. Here B satisfies both the conditions \[i.e.\] angles are in A.P. with common difference \[{{10}^{o}}\]and sum of angles is\[{{360}^{o}}\].

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