1. **State the problem:** We have an isosceles triangle with one obtuse angle and two equal acute angles. The obtuse angle measure is 2.5 times one acute angle. 2. **Define variables:** Let $x$ be the measure of one acute angle. Let $y$ be the measure of the obtuse angle. 3. **Write the system of equations:** - Since the triangle is isosceles, the two acute angles are equal: $x$ and $x$. - The obtuse angle is $y = 2.5x$. - The sum of angles in a triangle is $180^\circ$, so: $$2x + y = 180$$ 4. **Substitute $y$ from the first equation into the second:** $$2x + 2.5x = 180$$ 5. **Combine like terms:** $$4.5x = 180$$ 6. **Solve for $x$:** $$x = \frac{180}{4.5}$$ $$x = 40$$ 7. **Find $y$ using $y = 2.5x$:** $$y = 2.5 \times 40 = 100$$ 8. **Conclusion:** - Each acute angle measures $40^\circ$. - The obtuse angle measures $100^\circ$. This satisfies the triangle angle sum and the given ratio.