1. **Problem statement:** For diagram (a), two rays form a V-angle with angles labeled $5x$ and $4x$. We need to write an equation involving these angles, simplify, solve for $x$, find the angle sizes, and verify the solution. 2. **Formula and rules:** The sum of angles around a point on a straight line is $180^\circ$. 3. **Write the equation:** Since the two angles form a straight angle, $$5x + 4x = 180$$ 4. **Simplify the equation:** $$9x = 180$$ 5. **Solve for $x$:** $$x = \frac{180}{9}$$ $$x = 20$$ 6. **Find the angle sizes:** - Left angle: $5x = 5 \times 20 = 100^\circ$ - Right angle: $4x = 4 \times 20 = 80^\circ$ 7. **Check the solution:** Substitute $x=20$ back into the original equation: $$5(20) + 4(20) = 100 + 80 = 180$$ This matches the straight angle, so the solution is correct. **Final answer:** $x=20$, angles are $100^\circ$ and $80^\circ$.