Task 1. The arc above the base of an isosceles triangle is $\frac{2}{5}$ of the circumscribed circle of that triangle. Find the angles of that triangle.
Solution. The central angle over the base is $\frac{2}{5} \cdot 360^{\circ}=144^{\circ}$. Then the angle of the triangle opposite the base is $72^{\circ}$, and the angles at the base are $\frac{180-72}{2}=54^{\circ}$.