1. **State the problem:** We have a quadrilateral with two known angles: 96° and 110°, and two missing angles labeled 1 and 2. We need to find the values of angles 1 and 2. 2. **Recall the formula:** The sum of interior angles in any quadrilateral is always $$360^\circ$$. 3. **Set up the equation:** Let angle 1 be $x$ and angle 2 be $y$. Then, $$x + y + 96 + 110 = 360$$ 4. **Simplify the known angles:** $$x + y + 206 = 360$$ 5. **Isolate $x + y$:** $$x + y = 360 - 206$$ $$x + y = 154$$ 6. **Use the property of the quadrilateral with pairs of equal sides:** Since the quadrilateral has two pairs of equal sides, it is a kite, and the angles between unequal sides are equal. Therefore, angles 1 and 2 are equal: $$x = y$$ 7. **Substitute $y$ with $x$:** $$x + x = 154$$ $$2x = 154$$ 8. **Solve for $x$:** $$x = \frac{154}{2}$$ $$x = 77$$ 9. **Conclusion:** Angle 1 is $$77^\circ$$ and angle 2 is $$77^\circ$$.