Question

the conjecture \for n > 3, all n - gons have an even number of sides\ is disproved by which statement? a hexagons have six sides. b pentagons have five sides. c octagons have eight sides. d quadrilaterals have four sides.

Explanation:

Step1: Analyze the conjecture

The conjecture is that for \(n>3\), all \(n -\)gons have an even number of sides.

Step2: Check each option

A hexagon (\(n = 6\)) has an even number of sides, so it does not disprove the conjecture. An octagon (\(n=8\)) has an even number of sides and does not disprove it. A quadrilateral (\(n = 4\)) has an even number of sides and does not disprove it. A pentagon (\(n=5\)) has an odd - number of sides and \(5>3\), so it disproves the conjecture.

Answer:

B. Pentagons have five sides.