Question

Find the number of triangles through a vertex and the sum of their angles in an
octagon.​

Answer 1

Answer:

The number of triangles is 1, 8, 35, 110, 287, 632, 1302, 2400, 4257, 6956 for polygons with 3 through 12 sides. If we connect all vertices of a regular N-sided polygon we obtain a figure with = N (N - 1) / 2 lines. For N=8, the figure is: Careful counting shows that there are 632 triangles in this eight sided figure.

Answer 2

Step-by-step explanation:

Octagon : 8 sided polygon

No three points are collinear

For a triangle three points are needed selecting three points of eight

n

C

r

=

(n−r)!r!

n!

8

C

3

⇒

5!×3!

8!

⇒

3×2

8×7×6

⇒56

Therefore 56 Triangles are possible