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
$$A=(n-2)\times {180}^{\circ }$$ 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 $$A=(n-2)\times {180}^{\circ }$$ . 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:
$$A=(n-2)\times {180}^{\circ }$$
$$\Rightarrow A=(7-2)\times {180}^{\circ }$$
$$\Rightarrow A=5\times {180}^{\circ }$$
$$\therefore A={900}^{\circ }$$
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:
$$\therefore A={\displaystyle \frac{{900}^{\circ }}{7}}=\text{128}\text{.5714285714286}\approx {129}^{\circ }$$
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 $${360}^{\circ }$$.