In the diagram, what is the measure of angle 1? a. 135° b. 125° c. 15° d. 45°

We know that
 angle (3x) and angle (9x) are supplementary angles
so
3x+9x=180°> 12x=180°> x=180°/12> x=15°

angle (9x) and angle (1) are supplementary angles
so
9x+∡1=180> 9*15+∡1=180
∡1=180-9*15> ∡1=180-135> ∡1=45°

the answer is
∡1 is 45°

alternative method
angle 1 = angle 3x> vertical angles
∡1=3x> 3*15> 45°