1. **State the problem:** We are given pairs of adjacent angles on a straight line. Adjacent angles on a straight line are supplementary, meaning their sum is 180°. 2. **Formula used:** For two adjacent angles $A$ and $B$ on a straight line, we have: $$A + B = 180^\circ$$ 3. **Solve part (a):** Angles are $7x$ and $2x$. $$7x + 2x = 180$$ $$9x = 180$$ $$x = \frac{180}{9}$$ $$x = 20$$ 4. **Solve part (b):** Angles are $8x + 50$ and $5x$. $$8x + 50 + 5x = 180$$ $$13x + 50 = 180$$ $$13x = 180 - 50$$ $$13x = 130$$ $$x = \frac{130}{13}$$ $$x = 10$$ 5. **Solve part (c):** Angles are $2x + 35$ and $7x + 10$. $$2x + 35 + 7x + 10 = 180$$ $$9x + 45 = 180$$ $$9x = 180 - 45$$ $$9x = 135$$ $$x = \frac{135}{9}$$ $$x = 15$$ **Final answers:** - (a) $x = 20$ - (b) $x = 10$ - (c) $x = 15$