The internal angles of a nonagon are 40° X 9 = 360. Of an octagon, 45° X 8 = 360°. Of a hexagon, 60° X 6 = 360°.

Question

Pentagon, 72° X 5 = 360°. A quadrilateral, 90° X 4 = 360°. Now we come to the triangle. The internal angles of a triangle equal only 180°. What. The. Blazes? Anybody out there have an explanation that makes sense?

Answer 1

assume that all polygons are regular, that is, all the angles have the same measure

use the formula (n-2)(180) to determine how many degrees are in each polygon

n=the number of sides

nonagon

(9-2)(180)=7*180=1260, 1260/9=140º in each angle

octagon

(8-2)(180)=6*180=1080, 1080/8=135º

hexagon

(6-2)(180)=4*180=720, 720/6=120º

pentagon

(5-2)(180)=3*180=540, 540/5=108º

and so on

if you draw pictures or look these polygons up on the internet you will see that for a pentagon, hexagon, octagon, nonagon, and so on, all the angles are obtuse angles (greater than 90º but less than 180º)

the angles you are giving are all acute angles; these angles do not make sense

are you thinking of the angles in the congruent triangles that you can draw ? if so you are still making mistakes except for the hexagon

all the angles that you are giving are the external angles of each of the polygons; find the interior angle like I did with the formula and then subtract that angle from 180 degrees and you will come up with the angles you are giving; the sum of the exterior angles in any polygon is 360 degrees for a triangle, 180-60=120, 120*3=360 degrees