Question

find the angle sum of an octagon​

Answer 1

Answer:

1080

Step-by-step explanation:

Answer 2

Answer:

Step-by-step explanation:

Now take a look at what you have. You should see six non-overlapping triangles stuck together to make an octagon. Notice how every angle in each of those triangles is part of one of the angles of the octagon. That means that if you add up all the angles in those six triangles, you'll get the total internal angle sum of the octagon.

In this case, 6 x 180 = 1080; an octagon's internal angles add up to 1080 degrees.

You can do this with any convex polygon, and by convex, I mean that all the internal angles are less than 180 degrees. If you do a little investigating, you'll find that the number of triangles is always two less than the number of sides. This is so regular that it's stated as a theorem:

If a convex polygon has n sides, then its interior angle sum (S) is given by the following equation:

S = ( n – 2) × 180°

With this equation, you can calculate the interior angle sum of polygons with 37 sides (6300 degrees), 73 sides (12,780 degrees), or even 100 sides (17,640 degrees) without knowing any other information.