1. **Stating the problem:** We are given a triangle with two equal sides and an included angle of 25° between them. We need to find the measures of angles 1 and 2. 2. **Important rule:** In an isosceles triangle (two equal sides), the angles opposite those sides are equal. 3. **Given:** The angle between the two equal sides is 25°. 4. **Step:** Let angles 1 and 2 be the base angles opposite the equal sides. Since the triangle's interior angles sum to 180°, we have: $$m\angle1 + m\angle2 + 25^\circ = 180^\circ$$ 5. **Since the triangle is isosceles,** $$m\angle1 = m\angle2 = y$$ 6. **Substitute:** $$y + y + 25 = 180$$ 7. **Simplify:** $$2y + 25 = 180$$ 8. **Isolate $y$:** $$2y = 180 - 25$$ $$2y = 155$$ 9. **Divide both sides by 2:** $$y = \frac{155}{2}$$ $$y = 77.5$$ 10. **Conclusion:** $$m\angle1 = m\angle2 = 77.5^\circ$$ Thus, the measures of angles 1 and 2 are both 77.5 degrees.