If L || M, find the value of each missing variable(s).

13. x = 21; y = 15

14. x = 8; y = 11

15. x = 16; y = 23

Step-by-step explanation:

13. (3x - 16)° + (6x + 7)° = 180° (same side interior angles are supplementary)

Solve for x

3x - 16 + 6x + 7 = 180

Collect like terms

9x - 9 = 180

Add 9 to both sides

9x = 180 + 9

9x = 189

Divide both sides by 9

x = 189/9

x = 21

(6x + 7)° = (11y - 32)° (vertical angles are congruent)

Solve for y by substituting x = 21 into the equation

6(21) + 7 = 11y - 32.

126 + 7 = 11y - 32

133 = 11y - 32

Add 32 to both sides

133 + 32 = 11y

165 = 11y

Divide both sides by 11

165/11 = y

15 = y

y = 15

14. (11x - 25)° = (8x - 1)° (alternate exterior angles theorem and corresponding angles theorem)

Solve for x

11x - 25 = 8x - 1

Collect like terms

11x - 8x = 25 - 1

3x = 24

Divide both sides by 3

x = 24/3

x = 8

(8x - 1)° + (15y - 48)° = 180° (linear pair theorem)

Substitute x = 8 into the equation and solve for y

8(8) - 1 + 15y - 48 = 180

64 - 1 + 15y - 48 = 180

15 + 15y = 180

Subtract 15 from both sides

15y = 180 - 15

15y = 165

Divide both sides by 15

y = 165/15

y = 11

15. (7x - 44)° = (4x + 4)° (alternate exterior angles theorem)

Solve for x

7x - 44 = 4x + 4

Collect like terms

7x - 4x = 44 + 4

3x = 48

Divide both sides by 3

x = 48/3

x = 16

39° + (8y - 43)° = 180° (corresponding angles theorem and linear pair theorem)

Solve for y

39 + 8y - 43 = 180

Collect like terms

-4 + 8y = 180

Add 4 to both sides

8y = 180 + 4

8y = 184

Divide both sides by 8

y = 184/8

y = 23

10 * 563.67 = 5636.7