1. **State the problem:** The angles of a triangle are in the ratio 1:3:5. We need to find the measure of the largest angle. 2. **Recall the rule:** The sum of the angles in any triangle is always 180°. 3. **Set up the equation:** Let the common ratio be $x$. Then the angles are $x$, $3x$, and $5x$. 4. **Write the sum equation:** $$x + 3x + 5x = 180$$ 5. **Simplify:** $$9x = 180$$ 6. **Solve for $x$:** $$x = \frac{180}{9} = 20$$ 7. **Find the largest angle:** $$5x = 5 \times 20 = 100$$ **Answer:** The largest angle measures 100°.