Find the measure of an angle in a regular polygon with 24 sides.

The angles inside a 24 sided regular polygon (icositetragon) are 82.5.

Step-by-step explanation:

It's pretty easy to work out an equation for the angles in a regular polygon given the number of sides.  Let's do it:

triangle: 60° × 3 = 180°

square: 90° × 4 = 360°

pentagon: 108° × 5 = 540°

hexagon: 120° × 6 = 720°

As you can see, the sum of the angles in each one is equal to 180 degrees times the number of sides minus two.  This does carry through consistently.

So to get the angle in a regular polygon with 24 sides, we can say:

a = 180(24 - 2) / 24

a = 180 × 22 / 24

a = 90 × 11 / 12

a = 990 / 12

a = 165 / 2

a = 82.5

So each angle in our icositetragon is 82.5 degrees.