Find the measure of the smaller angle in the figure

You know that the two angles make up a perfectly flat line, which is a 180° angle. So we can create the equation:'

3x + 10 = 12x

Now solve for 'x'. Subtract 3x to both sides:

10 = 9x

Divide 9 to both sides:

x = 10/9

We want to find the smaller angle, so put this value in for 'x' in '3x + 10':

3x + 10

3(10/9) + 10

30/9 + 10

13 1/3°