Question

Statement (1): Through each vertex of a hexagon, 3 diagonals can be drawn.

Statement (2): The number of diagonals through a vertex of a polygon = the number of sides in the polygon − 3.

Options

• Both the statements are true.

• Both the statements are false.

• Statement 1 is true, and statement 2 is false.

• Statement 1 is false, and statement 2 is true.

Answer 1

Both the statements are true.

Explanation:

• Statement (1): A hexagon has 6 sides (n = 6). Using the formula for the number of diagonals that can be drawn from a single vertex (n − 3), we get 6 − 3 = 3 diagonals, making Statement (1) true.
• Statement (2): From any single vertex of an $n$-sided polygon, a diagonal cannot be drawn to the vertex itself or to its two adjacent neighboring vertices. This leaves n − 3 valid vertices to connect, confirming that the formula “Number of sides in the polygon - 3” is correct.