Question

Find the number of sides of a convex polygon if the sum of the measures of its interior angles is: 540°, 1,080°, 1,800°, 1,620°, 2,340°, 3,600°, 2,880°, and 7,560°.

Answer 1

Explanation:

Part 1)

Part 2)

Part 3)

Part 4)

Part 5)

Part 6)

Part 7)

Part 8)

Explanation:

we know that

The formula to calculate the sum of the interior angles of a convex polygon is equal to

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

substitute in the formula

solve for n

Divide by 180° both sides

Adds 2 both sides

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

substitute in the formula

solve for n

Divide by 180° both sides

Adds 2 both sides

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

substitute in the formula

solve for n

Divide by 180° both sides

Adds 2 both sides

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

substitute in the formula

solve for n

Divide by 180° both sides

Adds 2 both sides

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

substitute in the formula

solve for n

Divide by 180° both sides

Adds 2 both sides

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

substitute in the formula

solve for n

Divide by 180° both sides

Adds 2 both sides

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

substitute in the formula

solve for n

Divide by 180° both sides

Adds 2 both sides

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

substitute in the formula

solve for n

Divide by 180° both sides

Adds 2 both sides

Answer 2

Part 1)
`n=5\ sides`

Part 2)
`n=8\ sides`

Part 3)
`n=12\ sides`

Part 4)
`n=11\ sides`

Part 5)
`n=15\ sides`

Part 6)
`n=22\ sides`

Part 7)
`n=18\ sides`

Part 8)
`n=44\ sides`

Explanation:

we know that

The formula to calculate the sum of the interior angles of a convex polygon is equal to

`S=(n-2)180^o`

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

`S=540^o`

substitute in the formula

`540^o=(n-2)180^o`

solve for n

Divide by 180° both sides

`3=(n-2)`

Adds 2 both sides

`n=5\ sides`

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

`S=1,080^o`

substitute in the formula

`1,090^o=(n-2)180^o`

solve for n

Divide by 180° both sides

`6=(n-2)`

Adds 2 both sides

`n=8\ sides`

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

`S=1,800^o`

substitute in the formula

`1,800^o=(n-2)180^o`

solve for n

Divide by 180° both sides

`10=(n-2)`

Adds 2 both sides

`n=12\ sides`

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

`S=1,620^o`

substitute in the formula

`1,620^o=(n-2)180^o`

solve for n

Divide by 180° both sides

`9=(n-2)`

Adds 2 both sides

`n=11\ sides`

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

`S=2,340^o`

substitute in the formula

`2,340^o=(n-2)180^o`

solve for n

Divide by 180° both sides

`13=(n-2)`

Adds 2 both sides

`n=15\ sides`

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

`S=3,600^o`

substitute in the formula

`3,600^o=(n-2)180^o`

solve for n

Divide by 180° both sides

`20=(n-2)`

Adds 2 both sides

`n=22\ sides`

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

`S=2,880^o`

substitute in the formula

`2,880^o=(n-2)180^o`

solve for n

Divide by 180° both sides

`16=(n-2)`

Adds 2 both sides

`n=18\ sides`

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

`S=7,560^o`

substitute in the formula

`7,560^o=(n-2)180^o`

solve for n

Divide by 180° both sides

`42=(n-2)`

Adds 2 both sides

`n=44\ sides`