1) always

2) sometimes

3) sometimes

4) sometimes

5) always

6) 20

7) 85

8) 5

9) 40

10) angles 1 and 2 form a linear pair - given

angle 1 + angle 2 = 180 degrees - definition of a linear pair

angles 1 and 2 are supplementary - definition of supplementary

11) ABC = EFG and ABD = EFH - Given

ABD + DBC = ABC and EFH + HFG = EFG - angle addition

EFH + HFG = ABC - substitution

ABD + HFG = ABC - substitution

DBC = ABC - ABD and HFG = ABC - ABD - substitution

DBC = HFG - transitive

12) 150

13) 150

14) 30

15) 30

16) 30

17) 150

18) 150

19) p || q - given

angle 1 is supplementary to angle 4 - adjacent angles are supplementary

angle 4 = angle 2 - alternate exterior angles congruent

angle 1 is supplementary to angle 2 - substitution

20) m || n - given

angle 4 is supplementary to angle 3 - adjacent angles are supplementary

angle 1 = angle 3 - corresponding angles are congruent

angle 4 is supplementary to angle 1 - substitution