1. **Stating the problem:** We need to find the angle $x$ in a quadrilateral with given angles $100^\circ$ and $126^\circ$ and two pairs of equal sides. 2. **Understanding the properties:** The quadrilateral has two pairs of equal sides, which suggests it might be a kite or an isosceles trapezoid. The angles adjacent to equal sides have special relationships. 3. **Using angle sum property:** The sum of interior angles in any quadrilateral is $$360^\circ$$. 4. **Label the angles:** Let the four angles be $100^\circ$, $x^\circ$, $126^\circ$, and the unknown angle $y^\circ$. 5. **Calculate $y$:** Using the sum of angles, $$100 + x + 126 + y = 360$$ $$x + y = 360 - 226 = 134$$ 6. **Using the property of equal sides:** Since the quadrilateral has two pairs of equal sides, the angles between those sides are equal. Therefore, $x = y$. 7. **Solve for $x$:** $$x + x = 134$$ $$2x = 134$$ $$x = \frac{134}{2} = 67$$ **Final answer:** $$\boxed{67^\circ}$$