Mathematics, 07.01.2020 04:31 ptrlvn01

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°.

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Answer from: Jamilia561

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) $n=44\ sides$

Step-by-step 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

$n=44\ sides$

Answer from: Quest

180

step-by-step explanation:

12-2=10

20-2=18

18x10=180

Answer from: Quest

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