Identify the sum of the interior angle measures of a convex dodecagon. !

choice D. 1800

Work Shown:

A dodecagon has 12 sides (do = 2, deca = 10, dodeca = do+deca = 2+10 = 12). An alternative name to "dodecagon" is "twelve-gon" in which we can write "12-gon" for short.

The value n is the number of sides, so n = 12 is plugged into the formula below

S = 180(n-2)

S = 180(12-2)

S = 180(10)

S = 1800

If this were a regular dodecagon (all sides congruent), then E = 360/n = 360/12 = 30 is the measure of each exterior angle. So 180-E = 180-30 = 150 is the measure of each interior angle. So n*(180-E) = n*150 = 12*150 = 1800 is another way to get the answer. Again this is only assuming that the figure is regular. Otherwise, you should use the formula mentioned earlier.

step-by-step explanation: