Question

What is the sum of internal angles measures of a $20gon$ ?

Answer 1

Hint: In this problem, we have to find the sum of the interior angles of a $20gon$ , also known as an icosagon. Here, we will use the formula for the sum of interior angles, which is $S={{180}^{\circ }}\left( n-2 \right)$ . In this formula, we will substitute the value of n as $20$ , and then slowly calculate it to find the answer.

Complete step-by-step answer:
We have to find the sum of the interior angles of a $20gon$ , also known as an icosagon. Let us presume that the icosagon in our problem is a convex one. We can say that $n=20$ . We will use the formula to find the sum of the interior angles of the polygon. The formula is,
$S={{180}^{\circ }}\left( n-2 \right)$
 Substituting the value of $n=20$ in this formula, we get,
$\Rightarrow S={{180}^{\circ }}\left( 20-2 \right)$
Subtracting the terms in the bracket, we get,
$\Rightarrow S={{180}^{\circ }}\times 18={{3240}^{\circ }}$
Therefore, we can conclude that the sum of interior angles of a $20$ sided polygon is ${{3240}^{\circ }}$ .

Note: Polygon is a figure which is made up of and bounded by line segments. For a polygon, the interior angles are the angle between two sides of the polygon which lies within the polygon. For convex polygons, it is less than ${{180}^{\circ }}$ but for concave polygons, it is more that ${{180}^{\circ }}$ . We should keep this in mind while solving. Also, we should remember that circle is not a polygon as it is not made up of line segments. The polygon with the minimum number of sides is a triangle and the number of sides that it has is three.