Find the measure of each exterior angle of each regular polygon.

decagon

pentagon

hexagon

15-gon

Every polygon can be divided into triangles like so: take a pentagon and draw a line to every vertice inside the pentagn. It will make up three triangles. The easy way to do it is subtract 2 from the amount of sides, so a pentagon has five sides, five minus two is three so there are three triangles in a pentagon. Then since every triangle has 180 degrees you would simply multiply the amount of triangles bty 180 and that's how many degrees are in the polygon. Now you know that a pentagon has 540 degrees and it also has five angles so each angle in a pentagon is 60 degrees. Next step is on a line there are 180 degrees so the exterior angles are 120 degrees each because the interior is 60.

decagon exterior angle: 36
hexagon ": 60
15-gon": 24

In summary to find the exterior angle of a polygon subtract the amount of the interior angle by 180 which can be gotten by subtracting 2 from the amount of sides, multiplying by 180 and dividing by number of sides.

To find the exterior angle of any regular polygon, divide 360 by the number of sides.

decagon = 10 sides, exterior angle = 360/10 = 36°
pentagon = 5 sides, exterior angle = 360/5 = 72°
hexagon = 6 sides, exterior angle = 360/6 = 60°
15-gon = 15 sides, exterior angle = 360/15 = 24°

The interior angle is the supplement of the exterior angle.

The total measure of each interior angle of a polygon of n sides is (n-2) * 180. As such, the measure of each interior angle would be (n-2)*180 / n.

decagon: (10-2)(180) / 10 = 144
penatgon: (5-2)(180) / 5 = 108
hexagon: (6-2)(180) / 6 = 120
15-gon: (15-2)(180) / 15 = 156

Best of luck!