1. **State the problem:** We have an isosceles triangle ABC with an angle of 130° at vertex B. We need to determine which statement about the angles is true. 2. **Recall properties of isosceles triangles:** In an isosceles triangle, two sides are equal, and the angles opposite those sides are equal. 3. **Identify equal angles:** Since angle B is 130°, the other two angles, A and C, must be equal because the triangle is isosceles and B is the vertex angle. 4. **Use the triangle angle sum formula:** The sum of interior angles in any triangle is 180°. $$m\angle A + m\angle B + m\angle C = 180^\circ$$ 5. **Substitute known values:** Let $m\angle A = m\angle C = x$ and $m\angle B = 130^\circ$. $$x + 130^\circ + x = 180^\circ$$ 6. **Simplify the equation:** $$2x + 130^\circ = 180^\circ$$ 7. **Isolate $x$:** $$2x = 180^\circ - 130^\circ$$ $$2x = 50^\circ$$ 8. **Divide both sides by 2:** $$x = \frac{50^\circ}{2}$$ $$x = 25^\circ$$ 9. **Conclusion:** $$m\angle A = 25^\circ \quad \text{and} \quad m\angle C = 25^\circ$$ 10. **Check the given options:** None of the options exactly state $m\angle A = 25^\circ$ and $m\angle C = 25^\circ$. However, the sum $m\angle A + m\angle C = 50^\circ$. - Option 1: $15^\circ$ and $35^\circ$ (sum 50° but angles not equal) - Option 2: $m\angle A + m\angle B = 155^\circ$ (25° + 130° = 155°, true) - Option 3: $m\angle A + m\angle C = 60^\circ$ (we found 50°, so false) - Option 4: $20^\circ$ and $30^\circ$ (sum 50°, but angles not equal) 11. **Answer:** The statement that must be true is $m\angle A + m\angle B = 155^\circ$. **Final answer:** $m\angle A + m\angle B = 155^\circ$