1. **State the problem:** We have a triangle with angles labeled as 63°, (8x - 17)°, and (3x + 2)°, and we are given that $x = 12$. We need to find the measures of all angles. 2. **Recall the triangle angle sum rule:** The sum of the interior angles of any triangle is always 180°. So, $$63 + (8x - 17) + (3x + 2) = 180$$ 3. **Substitute the value of $x$:** $$63 + (8 \times 12 - 17) + (3 \times 12 + 2) = 180$$ 4. **Calculate each term:** $$63 + (96 - 17) + (36 + 2) = 180$$ $$63 + 79 + 38 = 180$$ 5. **Sum the angles:** $$63 + 79 + 38 = 180$$ $$180 = 180$$ 6. **Conclusion:** The angles are 63°, 79°, and 38°, which satisfy the triangle angle sum property. **Final answer:** The angles of the triangle are 63°, 79°, and 38°.