Answer
The sum of the measures of the angles of a polygon with \[n\] sides is\[\left( n-2 \right)\times 180{}^\circ \].
Work Step by Step
A polygon is a two-dimensional figure which is of two types that is a regular polygon and an irregular polygon. A regular polygon is a figure in which all the sides are of the same length. In an irregular polygon, all sides are of different length. The name of the polygon is classified according to the number of sides it contains.
A polygon with three sides is called a triangle. A polygon with four sides is called rectangle or quadrilateral. With n number of sides, a polygon contains a number of triangles.
Each triangle has a sum of angles\[180{}^\circ \]. After completing a circle, an exterior angle of \[360{}^\circ \]is formed. Sum of measures of angles of a polygon can be computed with the below-mentioned formula;
\[\begin{align}
& \text{Measurement of angle}=n\times 180{}^\circ -360{}^\circ \\
& =\left( n-2 \right)\times 180{}^\circ
\end{align}\].
