Apolygon is broken up into 4 non-overlapping triangles by drawing lines from one vertex to all other non-adjacent vertices. what is the name of the polygon? a) octagon b) hexagon c) heptagon d) quadrilateral

Answer :

The Correct Option is B) Hexagon

Step-by-step explanation :

Let number of sides in a polygon be n

The triangles are created by drawing the diagonals from one vertex to all the others.

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

⇒ Number of triangles = number of sides in polygon - 2

⇒ Number of triangles = n - 2

⇒ n = 4 + 2

⇒ n = 6

And the polygon containing 6 sides is called Hexagon

Hence, the correct Option is B) Hexagon

b

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