1. **State the problem:** We have a linear pair of angles where one angle is 12 degrees less than half the other angle. We need to find both angles. 2. **Recall the property of a linear pair:** The sum of the two angles in a linear pair is 180 degrees. 3. **Define variables:** Let the larger angle be $x$ degrees. 4. **Express the other angle:** The other angle is $\frac{x}{2} - 12$ degrees. 5. **Set up the equation using the linear pair property:** $$x + \left(\frac{x}{2} - 12\right) = 180$$ 6. **Simplify the equation:** $$x + \frac{x}{2} - 12 = 180$$ $$\Rightarrow \frac{2x}{2} + \frac{x}{2} - 12 = 180$$ $$\Rightarrow \frac{3x}{2} - 12 = 180$$ 7. **Isolate the term with $x$:** $$\frac{3x}{2} = 180 + 12$$ $$\frac{3x}{2} = 192$$ 8. **Multiply both sides by 2 to clear the denominator:** $$\cancel{\frac{3x}{\cancel{2}}} \times 2 = 192 \times 2$$ $$3x = 384$$ 9. **Divide both sides by 3 to solve for $x$:** $$x = \frac{384}{3}$$ $$x = 128$$ 10. **Find the other angle:** $$\frac{x}{2} - 12 = \frac{128}{2} - 12 = 64 - 12 = 52$$ 11. **Check the sum:** $$128 + 52 = 180$$ which confirms the solution. **Final answer:** The two angles are $128^\circ$ and $52^\circ$.