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write an expression for the sum of the angle measures in a regular polygan with n sides. then wirte an expression for the measure of each angle in a regular polygan with n sides.

  • geometry -

    If it has n sides you make n right turns to get all the way around the outside and end up going the same direction you were going at the start.
    So each right turn is 360/n
    Each interior angle is the supplement of that right turn
    180 - (360/n)
    so each interior angle = (180 n -360)/n

    each = 180 (n-2)/n

    the sum is then 180(n-2)

    check that
    triangle 180 (3-2)= 180 sure enough 180
    square 180(4-2) = 360 yes

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