IGCSE

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Mr. Bee moderators
25/06/2018 at 02:53
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A polygon is a closed figure whose sides are straight lines. The above figure shows a six-sided polygon (a hexagon). Show that the sum of the angles of a hexagon, \(S^o\), is \(S^o= 540^o\).

Then, show that the generalized formula for the sum of the angles of an n-sided polygon is \(S^o= 180^o(n-2)\).
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    Alone 25/06/2018 at 07:10

    A B C D E F

    \(S^o=\)\(\angle\)BAF + \(\angle\)ABC + \(\angle\)BCD + \(\angle\)CDE + \(\angle\)DEF + \(\angle\)EFA

      =\(\angle\)AFB + \(\angle\)BAF + \(\angle\)ABF + \(\angle\)CBF + \(\angle\)BCF + \(\angle\)DCF + \(\angle\)CDF + \(\angle\)EDF + \(\angle\)DEF + \(\angle\)EFD + \(\angle\)CFD + \(\angle\)BFC

     =\(180^o+180^o+180^o+180^o=720^o\)

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    Mr. Bee moderators 25/06/2018 at 07:31

    Sory, I mistyped. It should've been \(720^o\) not \(540^o.\)