Respuesta :
Answer:
Part 1) [tex]n=5\ sides[/tex]
Part 2) [tex]n=8\ sides[/tex]
Part 3) [tex]n=12\ sides[/tex]
Part 4) [tex]n=11\ sides[/tex]
Part 5) [tex]n=15\ sides[/tex]
Part 6) [tex]n=22\ sides[/tex]
Part 7) [tex]n=18\ sides[/tex]
Part 8) [tex]n=44\ sides[/tex]
Step-by-step explanation:
we know that
The formula to calculate the sum of the interior angles of a convex polygon is equal to
[tex]S=(n-2)180^o[/tex]
where
n is the number of sides of the polygon
Part 1) Find the number of sides of a convex polygon if the sum of the measures of its interior angles is: 540°
we have
[tex]S=540^o[/tex]
substitute in the formula
[tex]540^o=(n-2)180^o[/tex]
solve for n
Divide by 180° both sides
[tex]3=(n-2)[/tex]
Adds 2 both sides
[tex]n=5\ sides[/tex]
Part 2) Find the number of sides of a convex polygon if the sum of the measures of its interior angles is: 1,080°
we have
[tex]S=1,080^o[/tex]
substitute in the formula
[tex]1,090^o=(n-2)180^o[/tex]
solve for n
Divide by 180° both sides
[tex]6=(n-2)[/tex]
Adds 2 both sides
[tex]n=8\ sides[/tex]
Part 3) Find the number of sides of a convex polygon if the sum of the measures of its interior angles is: 1,800°
we have
[tex]S=1,800^o[/tex]
substitute in the formula
[tex]1,800^o=(n-2)180^o[/tex]
solve for n
Divide by 180° both sides
[tex]10=(n-2)[/tex]
Adds 2 both sides
[tex]n=12\ sides[/tex]
Part 4) Find the number of sides of a convex polygon if the sum of the measures of its interior angles is: 1,620°
we have
[tex]S=1,620^o[/tex]
substitute in the formula
[tex]1,620^o=(n-2)180^o[/tex]
solve for n
Divide by 180° both sides
[tex]9=(n-2)[/tex]
Adds 2 both sides
[tex]n=11\ sides[/tex]
Part 5) Find the number of sides of a convex polygon if the sum of the measures of its interior angles is: 2,340°
we have
[tex]S=2,340^o[/tex]
substitute in the formula
[tex]2,340^o=(n-2)180^o[/tex]
solve for n
Divide by 180° both sides
[tex]13=(n-2)[/tex]
Adds 2 both sides
[tex]n=15\ sides[/tex]
Part 6) Find the number of sides of a convex polygon if the sum of the measures of its interior angles is: 3,600°
we have
[tex]S=3,600^o[/tex]
substitute in the formula
[tex]3,600^o=(n-2)180^o[/tex]
solve for n
Divide by 180° both sides
[tex]20=(n-2)[/tex]
Adds 2 both sides
[tex]n=22\ sides[/tex]
Part 7) Find the number of sides of a convex polygon if the sum of the measures of its interior angles is: 2,880°
we have
[tex]S=2,880^o[/tex]
substitute in the formula
[tex]2,880^o=(n-2)180^o[/tex]
solve for n
Divide by 180° both sides
[tex]16=(n-2)[/tex]
Adds 2 both sides
[tex]n=18\ sides[/tex]
Part 8) Find the number of sides of a convex polygon if the sum of the measures of its interior angles is: 7,560°
we have
[tex]S=7,560^o[/tex]
substitute in the formula
[tex]7,560^o=(n-2)180^o[/tex]
solve for n
Divide by 180° both sides
[tex]42=(n-2)[/tex]
Adds 2 both sides
[tex]n=44\ sides[/tex]
