Maths-
General
Easy
Question
Make a conjecture about the number of diagonals of a pentagon. Write a conjecture for the general case.
Hint:
Inductive Reasoning is the process of drawing a general conclusion by observing a pattern based on the observations and this conclusion is called conjecture.
Deductive reasoning is the process by which a person makes conclusions based on previously known facts.
The correct answer is: Hence, the number of diagonals in a polygon is (n(n-3))/2, where n is the number of sides of the polygon.
The diagonals of the pentagon can be drawn as
Conjecture for the number of diagonals of a pentagon: The number of diagonals in a pentagon is 5.
Let’s take triangle, quadrilateral, pentagon, and hexagon and count their number of diagonals
By seeing the figures the number of diagonals in triangle, quadrilateral, pentagon, and hexagon are 0, 2, 5, 9
So we can conclude a formula i.e 
, where n is the number of sides of the polygon.
Final Answer:
Hence, the number of diagonals in a polygon is , where n is the number of sides of the polygon.
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