Question

How many diagonals does a regular pentagon have?
A) $3$
B) $4$
C) $5$
D) $6$

Answer 1

Hint: According to the question we have to determine the number of diagonals of a regular polygon so, first of all we have to determine the total number of sides of the pentagon.
Now, to determine the number of diagonals of a regular polygon we have to use the formula as mentioned below:

Formula used: Number of diagonals $ = \dfrac{{n(n - 3)}}{2}.............(A)$
Where, n is the number of sides of the given pentagon.
Hence, with the help of the formula above we can easily determine the number of diagonals for the given pentagon.

Complete step-by-step solution:
Step 1: First of all we have to determine the number total number of sides of the polygon which can be obtained by with the help of the diagram of pentagon as given below:

Hence, from the diagram we can see that the total number of sides are n = 5.
Step 2: Now, to find the number of diagonals we have to apply the formula (A) as mentioned in the solution hint. On substituting the value of n in the formula,
$
   = \dfrac{{5(5 - 3)}}{2} \\
   = \dfrac{{5 \times 2}}{2} \\
   = 5
 $
Final solution: Hence, with the help of formula (A) as mentioned in the solution hint we have obtained the number of diagonals in a regular pentagon which are 5.

Therefore option (C) is correct.

Note: A pentagon is a polygon having five sides and having each the interior angle ${72^\circ}$ and with the help of the formula $\dfrac{{n(n - 3)}}{2}$ we can easily determine the total number of diagonals where n is the total number of sides.