Answer:
x = 8
y = 21
Step-by-step explanation:
(7x + 12)° and (12x - 28)° are alternate interior angles. Alternate interior angles are congruent. Therefore:
(7x + 12)° = (12x - 28)°
Solve for x
7x + 12 = 12x - 28
Collect like terms
7x - 12x = - 12 - 28
-5x = -40
Divide both sides by -5
-5x/-5 = -40/-5
x = 8
(12x - 28)° + (9y - 77)° = 180° (linear pair)
To find y, plug in the value for x = 8.
12(8) - 28 + 9y - 77 = 180
96 - 28 + 9y - 77 = 180
Combine like terms
- 9 + 9y = 180
Add 9 to both sides
-9 + 9y + 9 = 180 + 9
9y = 189
Divide both sides by 9
9y/9 = 189/9
y = 21
