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9th Class Mathematics Lines and Angles Question Bank Lines and angles

  • question_answer
    In the adjoining figure, \[\mathbf{AB}\parallel \mathbf{CD}\] and PQ, QR intersect AB and CD both at E, F and G, H respectively. Given that \[\angle \mathbf{PEB}=\mathbf{7}{{\mathbf{0}}^{{}^\circ }},\]\[\angle \mathbf{QHD}=\mathbf{13}{{\mathbf{0}}^{{}^\circ }}\]and \[\angle \,\mathbf{PQR=x}{}^\circ ,\] find the value of \[{{\mathbf{x}}^{{}^\circ }}\].

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

    B)  \[{{10}^{{}^\circ }}\]

    C)  \[{{20}^{{}^\circ }}\]

    D)  \[{{30}^{{}^\circ }}\]

    Correct Answer: C

    Solution :

    (c): \[\angle PGH={{70}^{{}^\circ }}\Rightarrow \angle QGH={{110}^{{}^\circ }}\] \[\angle QHD={{130}^{{}^\circ }}\Rightarrow \angle CHQ={{50}^{{}^\circ }}\] \[\therefore \]\[\angle x+{{110}^{{}^\circ }}+{{50}^{{}^\circ }}={{180}^{{}^\circ }}\] \[\Rightarrow \]\[\angle x={{20}^{{}^\circ }}\]                          


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