The sum of interior angles of a polygon is 2880 degrees

how many sides has the polygon?
how many triangles are there in the polygon?
if the polygon is regular find the size of each of its exterior angles?

The sum of the measures of the interior angles of a convex polygon with n sides is (n-2)180

now we just substitute

(n-2)180=2880
180n-360=2880
180n=3240
n=18

there are 18 sides

to know how many triangles you just subtract 2 from the number of sides ex 3 sides 1 triangle so there would be 16 triangles in this polygon

In regular polygons the exterior angles always add up to 360 degrees so we would just take 360 and divide by the number of sides (360/18) which would give you 20 degrees per side

NOTE: Any polygon has internal angles = (n-2)180 where n is the number of sides.
how many sides has the polygon?
Total internal angles = 2880 = (n-2)180
n-2 = 2880/180 = 16
n = 16=2 = 18 sides <= ans1

Number of triangles is equal to the number of sides.
Number of triangles in that polygon = n = 18 <= ans2

External angles:
NOTE: External angle of a polygon is given by (n-2)180 / n. So,
(n-2)180 / n :the value of n calculated as 18
= (18-2)180 / 18 = 16*180/18 = 160 degrees <= ans3