1. **State the problem:** We have an isosceles triangle with two equal acute angles and one obtuse angle. The obtuse angle is 2.5 times one of the acute angles. We need to find the measure of each angle. 2. **Set variables:** Let $x$ be the measure of each acute angle, and $y$ be the measure of the obtuse angle. 3. **Write equations:** Since the triangle's angles sum to 180 degrees, we have: $$2x + y = 180$$ Given the obtuse angle is 2.5 times an acute angle: $$y = 2.5x$$ 4. **Substitute $y$ in the sum equation:** $$2x + 2.5x = 180$$ $$4.5x = 180$$ 5. **Solve for $x$:** $$x = \frac{180}{4.5}$$ $$x = 40$$ 6. **Find $y$ using $y = 2.5x$:** $$y = 2.5 \times 40 = 100$$ 7. **Conclusion:** The acute angles each measure $40^\circ$, and the obtuse angle measures $100^\circ$. This satisfies the properties of an isosceles triangle and the given conditions.