Question

1. Find the sum of the measures of the interior

Answer 1

Answer:

A) Sum of angles in the 14-gon = $2160^{o}$

B) Sum of angles in the 16-gon = $2520^{o}$

Step-by-step explanation:

Convex polygon is one that has the value of its internal angles less than the sum of angles in a triangle. That is each interior angle is less than $180^{o}$.

Sum of angles in a polygon = (n - 2) x $180^{o}$

where n is the value of its number of sides.

So that;

A) 14-gon (which has 14 sides),

Sum of angles in the 14-gon = (14 - 2) x $180^{o}$

                                  = 12 x $180^{o}$

                                  = $2160^{o}$

The sum of the measure of the interior angles of the 14-gon is $2160^{o}$.

B) 16-gon (which has 16 sides),

Sum of angles in the 16-gon = (16 - 2) x $180^{o}$

                                    = 14 x $180^{o}$

                                    = $2520^{o}$

The sum of the measure of the interior angles of the 16-gon is $2520^{o}$.