1. **Problem statement:** (a) Given lines AB and CD intersect at O, with $\angle AOC = 68^\circ$, find $\angle BOD$ and explain why. 2. **Key fact:** When two lines intersect, opposite (vertical) angles are equal. 3. **Solution for (a):** Since $\angle AOC$ and $\angle BOD$ are vertical angles formed by intersecting lines AB and CD at O, they are equal. Therefore, $\angle BOD = 68^\circ$. 4. **Reason:** Vertical angles are always equal. --- 5. **Problem statement (b):** Given two parallel lines cut by a transversal, $\angle a = 4x - 10$ and $\angle b = x$ are co-interior angles. 6. **Key fact:** Co-interior angles on parallel lines are supplementary, so their sum is $180^\circ$. 7. **Equation:** $$4x - 10 + x = 180$$ This simplifies to: $$5x - 10 = 180$$ This is the required equation relating $x$ to the angles. --- **Final answers:** (a) $\angle BOD = 68^\circ$ because vertical angles are equal. (b) Equation: $5x - 10 = 180$.