Question

In the diagram, what is the measure of angle 1?

Answer 1

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°