1. **Stating the problem:** We have a triangle inscribed in a circle with angles 67°, 9°, and an unknown angle. Outside the circle, at one vertex of an extended triangle, there is an angle of 62°. We need to find the unknown angle inside the triangle. 2. **Recall the triangle angle sum rule:** The sum of the interior angles of any triangle is always 180°. So, $$\text{Angle}_1 + \text{Angle}_2 + \text{Angle}_3 = 180^\circ$$ 3. **Apply the rule to the known angles:** We know two angles inside the triangle: 67° and 9°. Let the unknown angle be $x$. $$67^\circ + 9^\circ + x = 180^\circ$$ 4. **Calculate the sum of known angles:** $$67^\circ + 9^\circ = 76^\circ$$ 5. **Solve for $x$:** $$x = 180^\circ - 76^\circ$$ $$x = 104^\circ$$ 6. **Interpretation:** The unknown angle inside the triangle is 104°. 7. **Note about the 62° angle outside the circle:** This angle is an exterior angle to the triangle. The exterior angle theorem states that an exterior angle equals the sum of the two opposite interior angles. Here, 62° should equal the sum of the two interior opposite angles, which are 67° and 9°, but since 67° + 9° = 76°, this suggests the 62° angle is not directly related to the interior angles sum but is given as additional information. **Final answer:** The unknown angle inside the triangle is $\boxed{104^\circ}$.