If each interior angle of a rectangular polygon is 140º

If each interior angle of a rectangular polygon is 140º, then the number of vertices of the polygon is equal to
(a) 10
(b) 9
(c) 8
(d) 7

Anurag Mishra Professor Asked on 20th February 2016 in Maths.
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  • 1 Answer(s)

    Answer: (b) 9 

    Solution:-
    If each interior angle of a rectangular polygon is 140 degree

    Formula:-
    Each interior angle = 180 (n – 2)/n
    Where, n = number of sides. 

    Then, 140 = 180 (n – 2)/n
     7 = 9(n- 2)/n
    7 = (9 n – 18)/n
    By cross multiplication, 
    7 n = 9 n – 18
    9 n – 7 n = 18
    2 n = 18
    n = 18/2
    n = 9 

    Then, the number of vertices is 9.

    Hence, the correct answer is option (b) 9. 

    Anurag Mishra Professor Answered on 20th February 2016.
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