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

Answer:

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

$n=44\ sides$