In a regular pentagon, what is the relationship between the number of sides and the number of diagonals? (2023)
Practice Questions
1 question
Q1
In a regular pentagon, what is the relationship between the number of sides and the number of diagonals? (2023)
Diagonals are equal to sides.
Diagonals are twice the number of sides.
Diagonals are three times the number of sides.
Diagonals are less than the number of sides.
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.
Questions & Step-by-step Solutions
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Q
Q: In a regular pentagon, what is the relationship between the number of sides and the number of diagonals? (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.
Steps: 7
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.
