Two rays drawn from a point O form an angle of 145°. What is the measure of the reflex angle at O — the angle you turn through going the other way round?

The two angles at O together make one complete turn, which is 360°. So the reflex angle = 360 − 145 = 215°. It is more than 180°, as a reflex angle must be. Trap: 35° comes from subtracting from 180° instead of 360° — that would be the linear-pair partner, not the reflex angle going the other way round.