1. **Problem Statement:** Find the unknown angle $x$ in each polygon given the other interior angles. 2. **Formula:** The sum of interior angles of a polygon with $n$ sides is given by: $$\text{Sum of interior angles} = (n-2) \times 180^\circ$$ 3. **Left Polygon (Hexagon):** - Number of sides $n=6$ - Sum of interior angles: $$ (6-2) \times 180^\circ = 4 \times 180^\circ = 720^\circ $$ - Known angles: $70^\circ, 142^\circ, 130^\circ, 30^\circ, 141^\circ$ - Sum of known angles: $$70 + 142 + 130 + 30 + 141 = 513^\circ$$ - Find $x$: $$x = 720 - 513 = 207^\circ$$ 4. **Right Polygon (Star-shaped, 4 sides):** - Number of sides $n=4$ - Sum of interior angles: $$ (4-2) \times 180^\circ = 2 \times 180^\circ = 360^\circ $$ - Known angles: $20^\circ, 85^\circ, 34^\circ$ - Sum of known angles: $$20 + 85 + 34 = 139^\circ$$ - Find $x$: $$x = 360 - 139 = 221^\circ$$ **Final answers:** - Left polygon: $x = 207^\circ$ - Right polygon: $x = 221^\circ$