1. **State the problem:** The angles in a triangle are in the ratio 3 : 1 : 2. We need to find the size of each angle. 2. **Recall the rule:** The sum of the angles in any triangle is always $180^\circ$. 3. **Set up the equation:** Let the common ratio factor be $x$. Then the angles are $3x$, $1x$, and $2x$. 4. **Write the sum equation:** $$3x + 1x + 2x = 180$$ 5. **Simplify the left side:** $$6x = 180$$ 6. **Solve for $x$:** $$x = \frac{180}{6}$$ $$x = 30$$ 7. **Find each angle:** - First angle: $3x = 3 \times 30 = 90^\circ$ - Second angle: $1x = 1 \times 30 = 30^\circ$ - Third angle: $2x = 2 \times 30 = 60^\circ$ **Final answer:** The angles are $90^\circ$, $30^\circ$, and $60^\circ$.