The supplementary numbers of the questions with supplementary angles are;
7. Not supplementary, x = 10
8. Supplementary, x = 15
9. Supplementary
10. Not supplementary, x = -4/9
The details of the above solutions are presented as follows;
7. The angles, (7·x + 21)° and (9·x + 1)° are alternate interior angles. According to the alternate interior angles theorem, they are congruent, therefore, we get;
(7·x + 21)° = (9·x + 1)°
9·x - 7·x = 21 - 1
2·x = 20
x = 20/2
x = 10
8. The angles (5·x + 5)° and (6·x + 10)° are same side interior angles, and according to same side interior angles theorem, we get that the angles are supplementary, therefore;
(5·x + 5)° + (6·x + 10)° = 180°
11·x + 15 = 180
x = (180 - 15)/11
x = 15
9. The angle (20·x + 30)° and the other angle, blocked from view are same side exterior angles, therefore, they are supplementary
10. The angles (2·x + 10)° and (11·x + 14)° are alternate exterior angles, and according to the alternate exterior angles, they are congruent but may not be supplementary, therefore;
(2·x + 10)° = (11·x + 14)°
11·x - 2·x = 10 - 14
9·x = -4
x = -4/9