In a regular pentagon, what is the relationship between the number of sides and

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Question: In a regular pentagon, what is the relationship between the number of sides and the number of diagonals? (2023)

Options:

Correct Answer: Diagonals are equal to sides.

Exam Year: 2023

Solution:

In a regular pentagon, the number of diagonals is given by n(n-3)/2. For n=5, it results in 5(5-3)/2 = 5, which is equal to the number of sides.

In a regular pentagon, what is the relationship between the number of sides and the number of diagonals? (2023)

In a regular pentagon, what is the relationship between the number of sides and the number of diagonals? (2023)

Step 1: Understand what a regular pentagon is. A regular pentagon has 5 sides.
Step 2: Identify the formula for finding the number of diagonals in a polygon. The formula is n(n-3)/2, where n is the number of sides.
Step 3: Substitute the number of sides (n=5) into the formula: 5(5-3)/2.
Step 4: Calculate the expression inside the parentheses: 5-3 = 2.
Step 5: Multiply the result by 5: 5 * 2 = 10.
Step 6: Divide the result by 2: 10 / 2 = 5.
Step 7: Conclude that in a regular pentagon, the number of diagonals is 5, which is equal to the number of sides.

Diagonals in Polygons – Understanding how to calculate the number of diagonals in a polygon using the formula n(n-3)/2, where n is the number of sides.
Properties of Regular Polygons – Recognizing the characteristics of regular polygons, including equal sides and angles.