# 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).

Relevance

Hence

Hexagon(6) = 720

Heptagon(7) = 900

Octagon(8) = 1080

Nonagon(9) = 1260

Decagon(10) = 1440

Hendecagon(11) = 1620

Dodecagon(12) = 1800

• 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

• 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

:)>

• 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.