How many diagonals does a regular pentagon have?

A. 3

B. 4

C. 5

D. 6

To determine how many diagonals a regular pentagon has, we can use a mathematical formula that applies to any polygon. The formula for calculating the number of diagonals in a polygon is given by:

Diagonal Formula

The formula is:

D = n(n - 3) / 2

Where D represents the number of diagonals and n is the number of sides in the polygon.

Applying the Formula to a Pentagon

A regular pentagon has 5 sides, so we can substitute n = 5 into the formula:

D = 5(5 - 3) / 2

This simplifies to:

D = 5(2) / 2

Which further simplifies to:

D = 10 / 2 = 5

Understanding the Result

This means that a regular pentagon has 5 diagonals. To visualize this, imagine connecting non-adjacent vertices of the pentagon. Each vertex connects to two other vertices that are not adjacent, creating a diagonal. Since there are 5 vertices, and each can connect to 2 others, we initially think there are 10 connections. However, since each diagonal is counted twice (once from each end), we divide by 2, resulting in 5 unique diagonals.

Summary of Options

• A. 3
• B. 4
• C. 5
• D. 6

Based on our calculations, the correct answer is C. 5.