Answer:
The measure of the sum of interior angles of a 11-gon is [tex]1620^{o}[/tex].
Each interior angle is approximately [tex]147.273^{o}[/tex].
Step-by-step explanation:
A convex polygon has the measure of each interior angles to be less than [tex]180^{o}[/tex].
But,
sum of interior angles of polygon = (n - 2) x [tex]180^{o}[/tex]
where n is the number of sides of the polygon.
For a convex 11-gon, we have;
sum of angles of a 11-gon = (11 - 2) x [tex]180^{o}[/tex]
= 9 x [tex]180^{o}[/tex]
= [tex]1620^{o}[/tex]
Sum of angles of a 11-gon = [tex]1620^{o}[/tex]
To check: convex polygons' interior angles are less than [tex]180^{o}[/tex].
so that,
each interior angle of 11-gon = [tex]\frac{1620}{11}[/tex]
= [tex]147.273^{o}[/tex]
