Question

How do you find the sum of the interior angle measures of a convex 16gon?

Answer 1

Hint: Here we will substitute the given number of sides in the formula of the sum of interior angles of a polygon. We will simplify the equation further to get the required sum of all the angles. A polygon is a two-dimensional geometrical figure that is formed by connecting a number of straight-line segments.

Formula Used:
Sum of Interior angles of a polygon \[ = {180^ \circ }\left( {n - 2} \right)\], where, \[n = \] number of sides.

Complete step-by-step answer:
We have to find the sum of the interior angle of the convex 16-sided polygon which is also known as (hexakaidecagon).
So, \[n = 16\]
We will use the formula for the sum of the interior angle of the polygon.
Substituting the value of \[n\] in the formula Sum of Interior angles of a polygon\[ = {180^ \circ }\left( {n - 2} \right)\], we get
Sum of Interior angles of a convex 16-gon \[ = {180^ \circ }\left( {16 - 2} \right)\]
Subtracting the terms, we get
\[ \Rightarrow \] Sum of Interior angles of a convex 16-gon \[ = {180^ \circ } \times 14 = {2520^ \circ }\]

Therefore, the sum of interior angles of a convex 16 sided polygon is \[{2520^ \circ }\].

Note:
The line segments used to form a polygon are called its sides and edges and the point at which two edges meet is known as vertices. The exterior angle of a polygon is the supplementary angle to the interior angles. As a polygon is a closed figure therefore there must be three line segments to form a polygon. There are different types of polygon based on the number of sides such as triangle, square, rectangle, hexagon, etc. We need to remember that a circle is not a polygon because the circle is formed by a curve and not a straight line segment.