Question

. The number of triangles formed by drawing diagonals

from one vertex of a polygon is 18. Then

a) what is the sum of angles of the polygon?​

Answer 1

Answer:

If the polygon has 'n' sides, then the number of triangle in a polygon is (n – 2). In a triangle there are three sides. In the adjoining figure of a triangle ABC we can observe that the number of triangles contained = 3 – 2 = 1.

hope this helps:)

Answer 2

Step-by-step explanation:

The triangles are created by drawing the diagonals from one vertex to all the others. Since there would be no diagonal drawn back to itself, and the diagonals to each adjacent vertex would lie on top of the adjacent sides, the number of diagonals from a single vertex is three less the the number of sides, or n-3. The number of triangles is one more than that, so n-2.

This can be used as another way to calculate the sum of the interior angles of a polygon. The interior angles of a triangle always sum to 180°. The number of triangles is n-2 (above). Therefor the interior angles of the polygon must be the sum of all the triangles' interior angles