1. **State the problem:** We are given two pairs of parallel diagonal lines crossing, with one angle marked 51° and the adjacent angle marked $a^\circ$. We need to find the value of $a$. 2. **Formula and rules:** When two lines intersect, the opposite (vertical) angles are equal. Also, adjacent angles on a straight line sum to 180°. 3. **Apply the rule:** Since the lines are parallel and intersecting, the angle adjacent to 51° on the same straight line is supplementary to 51°. Therefore, $$a + 51 = 180$$ 4. **Solve for $a$:** $$a = 180 - 51$$ $$a = 129$$ 5. **Conclusion:** The value of $a$ is 129°.