Question

What is the sum of all interior angles of a regular heptagon?

Answer 1

Hint: Here the given question is about to find the sum of all interior angles of a regular heptagon. Before finding that, let us know about a regular heptagon:
A heptagon has any 7-sided polygon. Since it has 7 sides, its name has a prefix ‘hept’ and hence it is known as heptagon. A regular heptagon is shown as below

Complete step by step solution:

For finding, the sum of all interior angles of any polygon, we will use the formula
\[A=\left( n-2 \right)\times {{180}^{\circ }}\] where ‘A’ is the sum of interior angles of a polygon and ‘n’ is the number of sides.
Let us solve the given question.
Now, we have to find the sum of the interior angles of a heptagon.
We already know that the sum of interior angles ‘A’ of any polygon of ‘n’ sides is given by the formula \[A=\left( n-2 \right)\times {{180}^{\circ }}\] . Hence, we will use this formula to find the required answer i.e., sum.
We know that a heptagon has 7 sides. Thus, \[n=7\].
Substituting the value of ‘n’ in the mentioned formula, we get:
\[A=\left( n-2 \right)\times {{180}^{\circ }}\]
\[\Rightarrow A=\left( 7-2 \right)\times {{180}^{\circ }}\]
\[\Rightarrow A=5\times {{180}^{\circ }}\]
\[\therefore A={{900}^{\circ }}\]
Therefore, the sum of all interior angles of a heptagon is \[{{900}^{\circ }}\].
Now, let us find out the measure of each angle in a regular heptagon.
Sum of the angles of a heptagon =\[{{900}^{\circ }}\]
Number of sides in a heptagon= 7
Hence, measure of each angle of a regular heptagon is give as:
\[\therefore A=\dfrac{{{900}^{\circ }}}{7}=\text{128}\text{.5714285714286}\approx {{129}^{\circ }}\]
Therefore, the measure of each angle of a regular heptagon is \[{{129}^{\circ }}\].

Note: We must know about the sum of the interior angles of the basic polygons as:
TRIANGLE has the sum of the interior angles is \[{{180}^{\circ }}\].
PENTAGON has the sum of the interior angles is \[{{360}^{\circ }}\].