Question

What is a regular polygon of 7 sides called? What is the sum of interior angles of a regular octagon?
\[\begin{align}
  & \text{(A) Heptagon,180} \\
 & (\text{B) Heptagon, 1080} \\
 & (\text{C) Heptagon,108} \\
 & \text{(D) Heptagon,100} \\
\end{align}\]

Answer 1

Hint: First we should draw the diagram of a 7-sided polygon. Now we will find the name of a 7-sided polygon. We know that an 8-sided polygon is said to be an octagon. Now we should assume the number of sides of an 8-sided polygon. Let us assume this equation as equation (1). We know that the sum of interior angles of a n-sided polygon is equal to \[(n-2)180\]. Let us assume this equation as equation (2). Now we should substitute equation (1) in equation (2). This will give us the sum of internal angles of a regular octagon.

Complete step-by-step answer:

This diagram represents a heptagon.
From this diagram, we can say that the regular polygon of 7 sides is called a heptagon.
In the question, we were given that to find the sum of interior angles of a regular octagon. We know that an 8-sided polygon is said to be an octagon.

It is clear for us that the above diagram represents an octagon.
\[\Rightarrow n=8...(1)\]
Let us assume that the sum of interior angles of regular n-sided polygon is equal to A, then
\[\Rightarrow A=(n-2)180....(2)\]
So, from equation (1) and equation (2), we will find the sum of interior angles of an octagon.
\[\begin{align}
  & \Rightarrow A=(8-2)(180) \\
 & \Rightarrow A=1080 \\
\end{align}\].
So, it is clear that the sum of interior angles of an octagon is equal to 1080.
Hence, we can say that option (B) is correct.

Note: Students generally read this type of question in an incorrect manner. They may read that it was given to find the sum of interior angles of a regular heptagon.
This process gives us the value of n is equal to 7.
We know that the sum of interior angles of regular n-sided polygon is equal to A, then
\[\Rightarrow A=(n-2)180\].
So, the sum of interior angles of a 7-sided polygon \[=(5)(180)=900\].
This will give us a wrong answer.