Triangle Largest Angle 3B3Cf9

1. **State the problem:** We are given that the angles in a triangle are in the ratio $1 : 2 : 9$ and we need to find the size of the largest 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 $1x$, $2x$, and $9x$. 4. **Write the sum equation:** $$1x + 2x + 9x = 180$$ 5. **Simplify the equation:** $$12x = 180$$ 6. **Solve for $x$:** $$x = \frac{180}{12}$$ $$x = 15$$ 7. **Find the largest angle:** The largest angle corresponds to $9x$: $$9 \times 15 = 135$$ **Answer:** The size of the largest angle is $135^\circ$.