1. **State the problem:** We are given a quadrilateral ABCD with interior angles $\angle A = 50^\circ$, $\angle B = 60^\circ$, $\angle C = 10^\circ$, and $\angle D = 70^\circ$. The diagonals intersect, creating angles of 110°, 70°, 70°, 30°, and 60° in the split triangles. We need to find the value of $x$, which is presumably one of these angles or related to them. 2. **Understand the properties:** The sum of interior angles in any quadrilateral is always $360^\circ$. The diagonals intersect and form vertical angles which are equal. Also, angles around a point sum to $360^\circ$. 3. **Use the given angles:** The diagonal intersection angles are given as 110° and 70°, 70° and 30°, and 60° in the split triangles. Since vertical angles are equal, the pairs 110° and 70° are vertical angles, and 70° and 30° are vertical angles. 4. **Calculate missing angles:** Since the angles around the intersection point sum to $360^\circ$, we have: $$110^\circ + 70^\circ + 70^\circ + 30^\circ = 280^\circ$$ The remaining angle at the intersection is: $$360^\circ - 280^\circ = 80^\circ$$ 5. **Identify $x$:** If $x$ corresponds to this missing angle at the intersection, then: $$x = 80^\circ$$ **Final answer:** $$x = 80^\circ$$