The formula for the sum of the interior angles of a polygon is (n-2)*180, where n is the number of sides.
So, you'd have:
180(24-2)
180(22)
3960
3960 degrees is the sum of all the measures of the interior angles of a 24-gon. Now, to find how much each angle measures in a regular 24-gon, simply divide this: 3960/24.
You can use a calculator to solve this, but to actually give you the answer to your question:
3960/24=165
In a regular 24-gon, each angle's measurement is 165 degrees.