At each vertex of a triangle one exterior angle is drawn. These three exterior angles are in the ratio 3 : 4 : 5. What is the smallest angle of the triangle itself?

Taking one exterior angle at each vertex, the three always total 360°, so 3k + 4k + 5k = 360° and k = 30°. The exterior angles are therefore 90°, 120° and 150°. Each interior angle is the supplement of its own exterior angle, giving 90°, 60° and 30°, which correctly add to 180°. The smallest interior angle sits at the LARGEST exterior angle, so it is 30°; pairing smallest with smallest wrongly gives 90°.