1. **Problem Statement:** Given triangle ABC with AB = AC and angle BAC = 26°, find the base angles and the exterior angle at vertex B. 2. **Formula and Rules:** In an isosceles triangle, two sides are equal, so the angles opposite those sides are equal. The sum of interior angles in any triangle is 180°. An exterior angle of a triangle equals the sum of the two opposite interior angles. 3. **Step-by-step Solution:** - Since AB = AC, triangle ABC is isosceles, so angles ABC and ACB are equal. Let each be $a$°. - Using the angle sum property: $$a + a + 26 = 180$$ $$2a + 26 = 180$$ $$2a = 180 - 26$$ $$2a = 154$$ - Divide both sides by 2: $$2\cancel{a} = 154$$ $$\cancel{2}a = 77$$ - So, $a = 77°$. - The exterior angle at vertex B, $x$, is the sum of the two opposite interior angles: $$x = 26 + 77 = 103°$$ **Final answers:** - Base angles $ABC = ACB = 77°$ - Exterior angle $DBC = 103°$