Let's say you know the measure of angle 10. Let's make it 120 degrees.
Since it looks like you're going through a traversals unit (or something that includes traversals), you know that angle 10 and angle 8 are the same, which means they are both 120 degrees.
Now, since a line is 180 degrees on one side, you have to subtract 180-120 to find angle 7, which is 60.
Using the exterior-interior rule (I don't know the name), you know that angle 7 is equal to angle 1, which gets you 60.
Angle 1: 60 degrees.
You can do the same thing with another angle to find 12, or continue with this scenario with angle 10 being 120 degrees.
Edit: If you want to continue with this scenario, you can use the two interior angle rule, where angle 9 is equal to angle 1, and angle 12 is equal to angle 5. This also means angle 13 is equal to angle 8. But, since angle 13 is also 120 degrees, and there are 180 degrees in a line, that means angle 12 is also 60 degrees.
Angle 12: 60 degrees.