Triangle ABC is inscribed in a circle. The arc BC not containing A, the arc CA not containing B and the arc AB not containing C are in the ratio 3 : 4 : 5. What is the largest angle of the triangle?

The twelve parts fill 360°, so one part is 30° and the arcs are 90°, 120° and 150°. Each angle of the triangle is an inscribed angle on the arc opposite it, so ∠A = 45°, ∠B = 60° and ∠C = 75°; these add to 180° as they must, and the largest is 75°. The trap 150° quotes the biggest arc rather than halving it, 90° assumes the largest arc must produce a right angle (that happens only when an arc is a full semicircle, 180°), and 60° picks the middle angle.