1. **State the problem:** Two angles are supplementary, meaning their measures add up to 180 degrees. One angle is twelve degrees more than twice the other angle. 2. **Define variables:** Let the measure of the first angle be $x$ degrees. 3. **Express the second angle:** The second angle is twelve degrees more than twice the first angle, so it is $2x + 12$ degrees. 4. **Write the equation for supplementary angles:** Since the angles are supplementary, their sum is 180 degrees: $$x + (2x + 12) = 180$$ 5. **Simplify the equation:** $$3x + 12 = 180$$ 6. **Solve for $x$:** $$3x = 180 - 12$$ $$3x = 168$$ $$x = \frac{168}{3} = 56$$ 7. **Find the second angle:** $$2x + 12 = 2(56) + 12 = 112 + 12 = 124$$ 8. **Answer:** The two angles measure $56$ degrees and $124$ degrees respectively.