1. **State the problem:** We have a trapezium ABCD with angles at vertices A, B, and D given as $y$, $100^\circ$, and $84^\circ$ respectively. We need to find the value of $y$. 2. **Recall the properties of a trapezium:** In a trapezium, one pair of opposite sides are parallel. Here, sides AB and DC are parallel. 3. **Use the property of consecutive interior angles:** When a transversal crosses two parallel lines, the consecutive interior angles are supplementary, meaning their sum is $180^\circ$. 4. **Identify the pairs of consecutive interior angles:** Since AB is parallel to DC, angles at A and D are consecutive interior angles, and angles at B and C are consecutive interior angles. 5. **Calculate angle at A:** Using the supplementary angle rule, $$y + 84^\circ = 180^\circ$$ 6. **Solve for $y$:** $$y = 180^\circ - 84^\circ = 96^\circ$$ 7. **Conclusion:** The value of $y$ is $96^\circ$.