Question

A polygon 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?octagonhexagonheptagonquadrilateral

Answer 1

The name of the polygon is (B) hexagon.

What is a hexagon?

• A hexagon is a six-sided polygon or 6-gon in geometry.
• The sum of any simple (non-self-intersecting) hexagon's internal angles is 720°.

To find the name of the polygon:

• Let the number of sides in a polygon be n.
• Triangles are formed by drawing diagonals from one vertex to each of the others.
• Because there is no overlapping of the triangles, no diagonal will be drawn back to itself, and the diagonals to each adjacent vertex will lie on top of the adjacent sides, so the number of diagonals from a single vertex is three less than the number of sides or n - 3, and the number of triangles is one more, or n - 2.

• Number of triangles = number of sides in polygon - 2
• Number of triangles = n - 2
• n = 4 + 2
• n = 6
• The polygon containing 6 sides is called a hexagon.

Therefore, the name of the polygon is (B) hexagon.

Know more about hexagon here:

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The complete question is given below:

A polygon 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