What is the measure of the interior angles of a regular 11-gon?

It is about 147 degrees. (147.27o)

Subtract 2 from the number of sides and multiply by 180 to see the sum of all the angles put together. Divide by the number of sides to get the measure of each angle by itself. That works for any number of sides as long as it's regular. So, 11-2=9 and 9*180=1620 and lastly 1620/11=147.272727
As a side note, to get straight to the measure of each individual angle you could also use 180-(360/x) where x is the number of sides.

In a regular 11-gon, sometimes called a hendecagon, each interior angle will be equivalent. The number of adjacent triangles that can be drawn inside a polygon of n sides is (n-2); for an 11-gon, that would be nine.

The sum of the angles in a triangle is always 180º, so the sum of angles in a hendecagon will be (9*180) which equals 1620 degrees. Since all interior angles are equal, divide 1620º by 11 to obtain the measure of each interior angle, about 147.27 degrees.

The also-equivalent exterior angle measurement is found by subtracting 147.27º from 180º -- each exterior angle is 32.73º.