1. **State the problem:** We need to find the value of the angle $x$ in a regular decagon (10-sided polygon) where $x$ is an interior angle formed by two triangles inside the decagon. 2. **Formula for interior angle of a regular polygon:** The measure of each interior angle of a regular polygon with $n$ sides is given by $$\text{Interior angle} = \frac{(n-2) \times 180}{n}$$ 3. **Calculate the interior angle of the decagon:** For $n=10$, $$\text{Interior angle} = \frac{(10-2) \times 180}{10} = \frac{8 \times 180}{10} = 144^\circ$$ 4. **Find the angle $x$:** The angle $x$ is related to the interior angle of the decagon and the angles formed by the triangles inside. Using the hint, $$x = 180^\circ - \frac{144^\circ}{2} = 180^\circ - 72^\circ = 108^\circ$$ 5. **Alternative approach using pentagon angles:** Recognize that the angle $x$ corresponds to an interior angle of a regular pentagon (5-sided polygon), where $$\text{Interior angle of pentagon} = \frac{(5-2) \times 180}{5} = \frac{3 \times 180}{5} = 108^\circ$$ **Final answer:** $$x = 108^\circ$$