Math hw help!!?

The sum of the interior angles of a triangle is 180 degrees, of a quadrilateral is 360, and a pentagon is 540 degrees. If the pattern continues, find the sum of the interior angles of a dodecagon (12 sides).

5 Answers

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  • 2 months ago
    Favourite answer

    For each additional side add 180 to the previous answer. 

    Hence  

    Hexagon(6) = 720 

    Heptagon(7) = 900

    Octagon(8) = 1080

    Nonagon(9) = 1260 

    Decagon(10) = 1440 

    Hendecagon(11) = 1620 

    Dodecagon(12) = 1800 

  • ?
    Lv 7
    2 months ago

    The sum of the interior angles of a triangle is 180 degrees, 

    of a quadrilateral is 360, and a pentagon is 540 degrees. 

    If the pattern continues, find the sum of 

    the interior angles of a dodecagon (12 sides).

    The general formula is [(n - 2) × 180]

    The sum of the interior angles of a dodecagon is 180o degrees

  • ?
    Lv 7
    2 months ago

    We have the sequence: 180, 360, 540,...for 3 sides, 4 side, 5 sides,...etc

    If we complete the sequence for 1 and 2 sides (even though not mathematically possible) we have:

    -180, 0, 180, 360, 540,...

    i.e. arithmetic with 1st term -180 and common difference 180

    so, nth term is -180 + 180(n - 1)

    i.e. 180n - 360 => 180(n - 2)...where n is the number of sides

    Hence, for a dodecagon we have:

    180(12 - 2) = 1800

    :)>

  • Jim
    Lv 7
    2 months ago

    The exterior angle is figured by 360/n

    Triangle has 3, so 360/3 = 120. Interior is thus 60 x 3 = 180

    In a formula this would be n(180 - 360/n)

    12(180 - 360/12) = 12(150) = 1800

    You can change the formula around for a simpler equation if desired.

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  • ted s
    Lv 7
    2 months ago

    the pattern is 180  ( x - 2) where x = the number of side....you SHOULD see that this is an arithmetical progression

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