Answer:
16. x = 18
17. y = 7.5
18. z = 7
Step-by-step explanation:
16. Same-side interior angles are supplementary, so add to give 180°.
... (8x-7) + (3x-11) = 180
... 11x = 198 . . . . . . . . . . collect terms, add 18
... x = 18 . . . . . . . . . . . . divide by 11
17. Alternate interior angles are equal.
... (2y+23) = (4y+8)
... 15 = 2y . . . . . . . . . add -2y-8
... 7.5 = y . . . . . . . . . . divide by 2
18. Same-side interior angles are supplementary, or linear angles are supplementary. Either way, ...
... (3z² -5) + 38 = 180 . . . . . . . . we know 2y+23 = 2·7.5+23 = 38 from 17.
... 3z² = 147 . . . . . . . . . . . . . . . . subtract 33
... z² = 49 . . . . . . . . . . . . . . . . . . divide by 3
... z = 7 . . . . . . . . . . . . . . . . . . . . take the positive square root
