Answer:
13. x = 21; y = 15
14. x = 8; y = 11
15. x = 16; y = 23
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