1. The problem is to find the angle of an isosceles triangle given some information. 2. An isosceles triangle has two equal sides and two equal angles opposite those sides. 3. The sum of all angles in any triangle is always $180^\circ$. 4. If the two equal angles are each $x$, then the third angle is $180^\circ - 2x$. 5. To find the angle, you need either the measure of the equal sides or one of the angles. 6. If you know the vertex angle (the angle between the two equal sides), then the base angles are each $\frac{180^\circ - \text{vertex angle}}{2}$. 7. If you know the base angles, the vertex angle is $180^\circ - 2 \times \text{base angle}$. 8. This formula helps you find any angle in an isosceles triangle once you know one angle or side. Final answer: Use the formula $$\text{vertex angle} = 180^\circ - 2 \times \text{base angle}$$ or $$\text{base angle} = \frac{180^\circ - \text{vertex angle}}{2}$$ depending on the known angle.