1. **State the problem:** We need to find the size of angle $\angle EDC$ in the given polygon with known angles at points $A$, $B$, $C$, and $E$. 2. **Given angles:** - $\angle B = 133^\circ$ - $\angle C$ has two adjacent angles: $126^\circ$ (blue) and $101^\circ$ (green) - $\angle A = 47^\circ$ - $\angle E = 62^\circ$ 3. **Important rules:** - The sum of interior angles in any polygon with $n$ sides is $$(n-2) \times 180^\circ$$. - Adjacent angles on a straight line sum to $180^\circ$. - Equal segments imply isosceles triangles or equal angles opposite those sides. 4. **Analyze angles at $C$:** The two angles at $C$ are $126^\circ$ and $101^\circ$. Since they are adjacent, their sum is: $$126^\circ + 101^\circ = 227^\circ$$ This exceeds $180^\circ$, so these must be angles on different sides or parts of the figure, not forming a straight line. 5. **Find the missing angle at $C$ related to $\angle EDC$:** Since $\angle EDC$ is at $D$, and $D$ is connected to $C$ and $E$, we consider triangle $CDE$. 6. **Sum of angles in triangle $CDE$:** $$\angle EDC + \angle DCE + \angle CED = 180^\circ$$ We know $\angle DCE$ corresponds to the $101^\circ$ green angle at $C$. $\angle CED$ corresponds to the $62^\circ$ angle at $E$. 7. **Calculate $\angle EDC$:** $$\angle EDC = 180^\circ - 101^\circ - 62^\circ = 17^\circ$$ **Final answer:** $$\boxed{17^\circ}$$