8th Class Mathematics Practical Geometry Question Bank Geometry

  • question_answer
    The interior angle of a regular polygon exceeds the exterior angle by\[\frac{AB}{BC}=\frac{PQ}{QR}\]. Then the number of sides in the polygon is

    A) 12                               

    B) 13

    C) 14                               

    D) 15

    Correct Answer: D

    Solution :

    Let the number of sides of polygon = n. Now, interior angle of polygon of n sides \[{{42}^{o}}\] And exterior angle of polygon of n sides \[{{48}^{o}}\] According to the equation, \[\angle BDC={{42}^{o}}\] \[\angle ACB\] \[\angle ACB={{65}^{o}}\] \[\angle ABC\] \[\left( 1-\frac{2}{n} \right)90{}^\circ =\frac{180{}^\circ }{n}+66{}^\circ \] \[{{35}^{o}}\] \[{{55}^{o}}\] \[{{208}^{o}}\] \[{{52}^{o}}\] \[\Delta XYZ\] \[\Delta XYZ\] \[{{60}^{o}}\]\[{{30}^{o}}\]


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