16. Vertical angles are the ones bounded by the same lines and have the same vertex, but that have no sides in common. Pairs 1 and 3 or 2 and 4 are vertical angles.
17. The diagram shows the sum of the three angles makes a right angle (90°). Write that as an equation:
... x° + 2x° + 15° = 90°
Solve the equation in the usual manner: collect terms, add the opposite of the unwanted constant on the left, divide by the coefficient of x.
... 3x° +15° = 90°
... 3x° = 75°
... x = 25
18. You may notice that this problem follows the same pattern as the one of 17. We add the constituent angles to make the whole right angle. Here, you have some follow-on effort to find ∠BDC after you find x.
... (-3x+20)° + (-2x+55)° = 90°
... -5x +75 = 90 . . . . . . . collect terms, divide by °
... -5x = 15 . . . . . . . . . . . subtract 75
... x = -3 . . . . . . . . . . . . . divide by the coefficient of x
Now we can find ∠BDC.
... ∠BDC = (-3x+20)° = (-3(-3)+20)°
... ∠BDC = 29°