1. **Problem:** Find the unknown angle $\angle U$ in kite $WVUT$ given $\angle V = 74^\circ$ and $\angle T = 96^\circ$. 2. **Properties of kites:** The sum of interior angles in any quadrilateral is $360^\circ$. In a kite, two pairs of adjacent sides are equal, and one pair of opposite angles are equal (angles between unequal sides). 3. **Formula:** $\angle W + \angle V + \angle T + \angle U = 360^\circ$. 4. **Calculation:** Given $\angle V = 74^\circ$, $\angle T = 96^\circ$, and $\angle W = \angle U$ (since they are opposite angles between equal sides in kite), let $\angle W = \angle U = x$. 5. Write equation: $$x + 74 + 96 + x = 360$$ 6. Simplify: $$2x + 170 = 360$$ 7. Solve for $x$: $$2x = 360 - 170 = 190$$ $$x = \frac{190}{2} = 95$$ 8. **Answer:** $\angle U = 95^\circ$. This uses the property that in a kite, the angles between the pairs of equal sides are equal, and the sum of all angles is 360 degrees.