Question

The number of diagonals drawn from one vertex of a polygon of \[n\] sides is _________.
A.\[\left( {n - 1} \right)\]
B.\[\left( {n - 2} \right)\]
C.\[\left( {n - 3} \right)\]
D.\[n\]

Answer 1

Hint: We will first consider the definition of the diagonal. As we have asked to find the number of diagonals drawn from one vertex of the polygon of \[n\] sides so, we will use the fact that the number of diagonals in a polygon drawn from any vertex is 3 less than the number of sides. As we are given that the number of sides in a polygon is \[n\] so, we will obtain the number of diagonals drawn from any vertex by subtracting 3 from the number of sides. Hence, we will get the desired result.

Complete step by step Answer:

We will first consider the definition of diagonal which states that a diagonal is a segment that connects two non-consecutive vertices in the polygon.
We need to determine the number of diagonals drawn from one vertex of a polygon of \[n\] sides.
Thus, as we know that the number of diagonals in a polygon that can be drawn from any vertex in the polygon is three less than the number of sides of the polygon.
Now, we are given in the question that the number of sides in the polygon is \[n\].
So, we will find the number of diagonals drawn from one vertex of the polygon of \[n\] sides by subtracting 3 from \[n\].
Thus, we get,
\[ \Rightarrow n - 3\]
Hence, the number of diagonals drawn in the polygon from each vertex of \[n\] sides is \[n - 3\] diagonals.
Thus, option C is correct.

Note: Remember the definition of diagonal. Also, the number of diagonals drawn in a polygon is always less than the number of sides of the polygon. For a convex \[n\]-sided polygon, there are \[n\] vertices \[n - 3\] and from each vertex we can draw \[n - 3\] diagonals. So, if we want to calculate the total number of diagonals in the figure, we just have to multiply \[n\] by that is \[n\left( {n - 3} \right)\].