Answer:
11. x=110 y=110
12. x=115 y=115
13. x=90 y=90
14. x=80 y=80
15. x=60 y=60
16. x=50 y=50
17. x=45
18. x=20
19. x=40
Explanation:
11. Supplementary angles add up to 180. x is the supplement to the angle labeled 70. 180-70=110, so x=110. y is a corresponding angle to x, which means they are congruent, so y=110.
12. Vertical angles are congruent. x is the vertical angle to the angle labled 115, so x=115. y is a corresponding angle to x, which means they are congruent, so y=115.
13. The square means that the labeled angle measures 90 degrees. x is a corresponding angle to the labeled angle, making them congruent, so x=90. y is supplementary to x, meaning that the measures of both angles add up to 180. 180-90=90, so y=90.
14. The angle labeled 100 and y are supplementary angles, so they add up to 180. 180-100=80, so y=80. y and x are alternate interior angles, so they are congruent. This means that x=80.
15. The angle labeled 120 and x are consecutive interior angles, meaning they are supplementary and add up to 180. 180-120=60, so x=60. x and y are vertical angles, which are congruent, so y=60.
16. The angle labeled 130 and x are consecutive interior angles, meaning they are supplementary and add up to 180. 180-130=50, so x=50. x and y are alternate exterior angles, which are congruent, so y=50.
17. The angles labeled (2x-10) and 80 are alternate interior angles, meaning they are congruent. This means we can set up the equation 2x-10=80 to find the value of x. When solved, x=45. You can plug the value of x back in to check.
18. The angles labeled 120 and 3x are consecutive interior angles, so they are supplementary. This means we can set up the equation 120+3x=180 to find the value of x. When solved, x=20. You can plug the value of x back in to check.
19. The angles labeled 135 and (3x+15) are corresponding angles, so they are congruent. This means we can set up the equation 135=3x+15 to find the value of x. When solved, x=40. You can plug the value of x back in to check.