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8th Class Mathematics Understanding Quadrilaterals Question Bank Understanding Quadrilaterals

  • question_answer
    In the given figure, line RT is drawn parallel to SQ. If\[\angle QPS=100{}^\circ \], \[\angle POS\text{ }=\text{ }40{}^\circ \], \[\angle PSR=85{}^\circ \] and\[\angle QRS=70{}^\circ \], then \[\angle QRT=\_\_\_\_\_\_\_\].

    A)  \[\text{45 }\!\!{}^\circ\!\!\text{ }\]                            

    B)  \[65{}^\circ \]          

    C)         \[\text{85 }\!\!{}^\circ\!\!\text{ }\]                

    D)         \[\text{90 }\!\!{}^\circ\!\!\text{ }\]                

    Correct Answer: B

    Solution :

    In\[\Delta \text{PQS}\], we have \[\angle PSQ=180{}^\circ -(100{}^\circ +40{}^\circ )=180{}^\circ -140{}^\circ =40{}^\circ \]Also, \[\angle PSR=85{}^\circ \] or \[40{}^\circ +\angle QSR=85{}^\circ \] \[\therefore \angle QSR=85{}^\circ -40{}^\circ =45{}^\circ \] A s \[\text{SQ }\!\!|\!\!\text{  }\!\!|\!\!\text{ RT}\] \[\therefore \angle QSR=\angle TRU=45{}^\circ \]                         (corresponding angles) So, \[\angle QRT=180{}^\circ -(70{}^\circ +45{}^\circ )\] (linear pair) \[=180{}^\circ -115{}^\circ =65{}^\circ \]


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