Find the value of each variable. x = y =

Solution:

1. Since the angles are vertical angles, they are equal. Set the expressions equal to each other:
2. Equation 1: 4x = 6x - 26
3. Solve for x:
4. 4x = 6x - 26
5. Subtract 4x from both sides: 0 = 2x - 26
6. Add 26 to both sides: 26 = 2x
7. Divide by 2: x = 13
8. Equation 2: 7y - 12 = 6y + 8
9. Solve for y:
10. 7y - 12 = 6y + 8
11. Subtract 6y from both sides: y - 12 = 8
12. Add 12 to both sides: y = 20

Final Answers:

x = 13

y = 20