1. **Stating the problem:** POR and QOR form a linear pair, meaning their angles add up to 180 degrees. Given that $a - b = 80$, find the values of $a$ and $b$. 2. **Formula and rules:** For a linear pair, the sum of the angles is 180 degrees: $$a + b = 180$$ Also given: $$a - b = 80$$ 3. **Explanation of the step $80 + b + b = 180$:** From the equation $a - b = 80$, we can express $a$ as: $$a = 80 + b$$ Substitute this into the linear pair equation: $$a + b = 180$$ becomes $$80 + b + b = 180$$ which simplifies to $$80 + 2b = 180$$ 4. **Solving for $b$:** $$80 + 2b = 180$$ Subtract 80 from both sides: $$\cancel{80} + 2b = 180 - \cancel{80}$$ $$2b = 100$$ Divide both sides by 2: $$\frac{\cancel{2}b}{\cancel{2}} = \frac{100}{2}$$ $$b = 50$$ 5. **Finding $a$:** Recall $a = 80 + b$: $$a = 80 + 50 = 130$$ **Final answer:** $$a = 130, \quad b = 50$$