Question

How many degrees does a pentagon have?

Answer 1

Hint:
Here we need to apply just the formula of the sum of all the interior angles of the polygon which says that
Sum of interior angles $ = \left( {n - 2} \right) \times 180^\circ $ where $n$ represents the number of sides of the polygon.

Complete step by step solution:
Here we are given to find the total degrees that a pentagon has. This total number of degrees means that we need to calculate the total sum of all the interior angles of the pentagon. We must know what pentagon is.
It is the polygon which has a total of $5$ sides.
We must know that sum of all the angle of the polygon is given by the formula $\left( {n - 2} \right) \times 180^\circ $
Here $n$ is representing the number of sides that the polygon has. As we know that pentagon is the polygon which has five sides so here we can say that $n = 5$
This is also valid for the triangle. In the triangle we know that $n = 3$ as there are three sides. So we can apply the formula and get:
Sum of interior angles$ = \left( {n - 2} \right) \times 180^\circ = \left( {3 - 2} \right) \times 180^\circ = 180^\circ $
In the similar way we can now find the sum of all the interior angles of the pentagon also. We need to use the same formula but now we will substitute $n = 5$ and we will get:
Sum of interior angles\[ = \left( {n - 2} \right) \times 180^\circ \]
Substituting $n = 5$ we will get:
Sum of interior angles\[ = \left( {n - 2} \right) \times 180^\circ = \left( {5 - 2} \right) \times 180^\circ = 3 \times 180^\circ = 540^\circ \]

Hence we get that sum of all the angles in the pentagon is \[540^\circ \]

Note:
Here if the student is given that it is the regular polygon then all the sides and angles will be equal and we can then calculate each interior angle by dividing the sum of all the interior angles by the number of sides.