The angles of a triangle are in ratio 2:3:4. Largest angle?

**The reasoning** The key principle here is that **all angles in a triangle sum to 180°**. Let the angles be 2x, 3x, and 4x (using the ratio 2:3:4). Setting up the equation: 2x + 3x + 4x = 180° 9x = 180° x = 20° Now find each angle: - Smallest angle = 2x = 2(20°) = 40° - Middle angle = 3x = 3(20°) = 60° - **Largest angle = 4x = 4(20°) = 80°** **Why the wrong options tempt you** **A) 40°** — This is actually the *smallest* angle (2x). You might pick this if you stop calculating after finding x and just double it without checking which is largest. **B) 60°** — This is the *middle* angle (3x). Easy to grab if you're rushing. **D) 100°** — Some students mistakenly add angles together (40° + 60°) instead of calculating 4x properly. **Quick takeaway** When angles are in a ratio, let them equal 2x, 3x, 4x (etc.), make them sum to 180°, solve for x, then multiply back to find the specific angle asked for—always the **biggest coefficient gives the largest angle**.