Question

1. Find the sum of the measures of the interior angles of a convex 11-gon.

Answer 1

Answer:

The measure of the sum of interior angles of a 11-gon is $1620^{o}$.

Each interior angle is approximately $147.273^{o}$.

Step-by-step explanation:

A convex polygon has the measure of each interior angles to be less than $180^{o}$.

But,

sum of interior angles of polygon = (n - 2) x $180^{o}$

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 $180^{o}$

                                         = 9 x $180^{o}$

                                         = $1620^{o}$

Sum of angles of a 11-gon = $1620^{o}$

To check: convex polygons' interior angles are less than $180^{o}$.

so that,

each interior angle of 11-gon = $\frac{1620}{11}$

                                        = $147.273^{o}$