The sum of the interior angles of an n gon is <span> (n-2)*180 the measure of each interior angle is </span><span>(n-2)*180/n the measure of each individual exterior angle of an ngon is 360/n all exterior angles add to 360
1. sum of 15 gon is (15-2)*180=13*180=2340 degrees
2. deca is 10 (10-2)*180/10=8*18=144 degrees
3. dodecagon is 12 sides 360/12=30 degrees
4. 4 sides, those are exterior angles, so they add to 360 4r+7r+8r+5r=360 24r=360 r=15 degrees
5. pentagon or 5 sides sum of internal is (5-2)*180=3*180=540 degrees 540=4z+5z+3z+5z+3z 540=20z 27 degrees=z 3z=81=A=D 4z=108=B 5z=135=C=E
8. interior angles of 4 gon sum is (4-2)*180=2*180=360 2n+6n+5n+2n=360 15n=360 n=24 2n=48 5n=120 6n=144
9. 6gon (6-2)*180=4*180=720 90+90+x+x+22+x+x+22=720 224+4x=720 minus 224 both sides 4x=496 divide by 4 x=124
10., exterior angle of pentagon, 5 gon 360/5=72=x
11. (n-2)*180/n=4*(360/n) times both sides by n (n-2)*180=4*360 divide both sides by 180 n-2=4*2 n-2=8 n=10 10 sides
12. area of octogon of side is </span>2(1+√2)s² where s is the side length given, 12=side length A=2(1+√2)12² A=2(1+√2)144² A=288(1+√2) A=288+288√2 square cm
