1. **Problem statement:** We are given a quadrilateral ABGD with AD parallel to BC. The angles at points G, D, and C are 60°, 70°, and 60° respectively, and we need to find the value of angle $x$ at point A. 2. **Key concept:** When two lines are parallel, alternate interior angles and corresponding angles formed by a transversal are equal. Also, the sum of angles in a triangle is always 180°. 3. **Step 1:** Consider triangle BCG formed by points B, C, and G. Since AD is parallel to BC, angle at G (60°) and angle at C (60°) are given. 4. **Step 2:** Calculate angle at B in triangle BCG: $$\text{Angle B} = 180^\circ - 60^\circ - 60^\circ = 60^\circ$$ 5. **Step 3:** Since AD is parallel to BC, angle at A ($x$) corresponds to angle at B (60°) because they are alternate interior angles. 6. **Final answer:** $$x = 60^\circ$$