Answer:
A) Sum of angles in the 14-gon = [tex]2160^{o}[/tex]
B) Sum of angles in the 16-gon = [tex]2520^{o}[/tex]
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 [tex]180^{o}[/tex].
Sum of angles in a polygon = (n - 2) x [tex]180^{o}[/tex]
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 [tex]180^{o}[/tex]
= 12 x [tex]180^{o}[/tex]
= [tex]2160^{o}[/tex]
The sum of the measure of the interior angles of the 14-gon is [tex]2160^{o}[/tex].
B) 16-gon (which has 16 sides),
Sum of angles in the 16-gon = (16 - 2) x [tex]180^{o}[/tex]
= 14 x [tex]180^{o}[/tex]
= [tex]2520^{o}[/tex]
The sum of the measure of the interior angles of the 16-gon is [tex]2520^{o}[/tex].
