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**Hint:**We here have been asked about the sum of the interior angles of a triangle. For finding that, let us first know about a pentagon:

A pentagon is any five-sided polygon. Since it has 5 sides, its name has a prefix ‘pent’ and hence known as pentagon. A regular pentagon is shown as follows:

Now, to find the sum of all interior angles of a pentagon, we will use the formula \[A=\left( n-2 \right)\times {{180}^{\circ }}\] where ‘A’ is the sum of interior angles of a polygon with ‘n’ sides.

**Complete step-by-step answer:**

Now, we have to find the sum of the interior angles of a pentagon.

We know that the sum of interior angles ‘A’ of any polygon of sides ‘n’ is given by the formula \[A=\left( n-2 \right)\times {{180}^{\circ }}\]. Thus, we will use this formula to find the required sum.

We know that a pentagon has 5 sides. Thus, $n=5$.

Putting the value of ‘n’ in the formula, we get:

\[\begin{align}

& A=\left( n-2 \right)\times {{180}^{\circ }} \\

& \Rightarrow A=\left( 5-2 \right)\times {{180}^{\circ }} \\

& \Rightarrow A=3\times {{180}^{\circ }} \\

\end{align}\]

\[\Rightarrow A={{540}^{\circ }}\]

Thus, the sum of interior angles of a pentagon is ${{540}^{\circ }}$.

Now, let us find out the measure of each angle in a regular pentagon.

We can find it through the following method:

We will divide the sum of the measures of the angles by the number of sides of the polygon.

Sum of the measure of the angles of a pentagon=${{540}^{\circ }}$

No. of sides in a pentagon= 5

Thus, measure of one angle of a regular pentagon is give as:

$\begin{align}

& \dfrac{{{540}^{\circ }}}{5} \\

& \Rightarrow {{108}^{\circ }} \\

\end{align}$

Therefore, the measure of one angle of a regular pentagon is 108°.

We can verify it by multiplying 108° by 5.

\[108{}^\circ \times 5=540{}^\circ \]

But this can only be calculated if the polygon is regular, i.e. we can only find the measure of one angle of a pentagon if the pentagon is a regular one, i.e., all of its sides are of the equal length.

Thus, the required answer is ${{540}^{\circ }}$.

**Note:**We must know the sum of the interior angles of the basic polygons as they can come in handy.

1. TRIANGLE: The sum of the interior angles of a triangle is always 180°.

2. QUADRILATERAL: The sum of the interior angles of a quadrilateral is always 360°.

3. PENATGON: The sum of the interior angles of a pentagon is always 540°.

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