50 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°.

540°,              5 =n

1,080°,             8 =n

1,800°              12 =n

1,620°,            11 =n

2,340°,             15 =n

3,600°,             22 =n

2,880°,             18 =n

7,560°             44 =n

Step-by-step explanation:

 sum of interior angle with n sides is (n – 2)180

540°,  540 = (n-2) *180

         540/180 = n-2

            3 = n-2

           5 =n

1,080°, 1080 = (n-2) *180

         1080/180 = n-2

            6 = n-2

           8 =n

1,800°  1800 = (n-2) *180

         1800/180 = n-2

            10 = n-2

           12 =n

1,620°, 1620 = (n-2) *180

         1620/180 = n-2

            9 = n-2

           11 =n

2,340°, 2340 = (n-2) *180

         2340/180 = n-2

            13 = n-2

           15 =n

3,600°, 3600 = (n-2) *180

         3600/180 = n-2

            20 = n-2

           22 =n

2,880°, 2880 = (n-2) *180

         2880/180 = n-2

            16 = n-2

           18 =n

7,560° 7560 = (n-2) *180

         7560/180 = n-2

            42 = n-2

           44 =n

a and c

for infinitely many solutions we require both left and right sides to be equal

distribute and simplify

a

14 - 8x = 20 - 8x - 6 = 14 - 8x ← both sides equal so infinite solutions

b

6x - 54 = 6x - 54 + x = 7x - 54 ← not equal

c

4x + 16 = 4x + 10 + 6 = 4x + 16 ← both sides equal so infinite solutions

d

5x - 40 + 10 = 5x + 10

5x - 30 = 5x + 10 ← not equal