Two complementary angles are such that twice the smaller angle exceeds the larger by 30°. Find the larger angle.

Let the larger angle be $x$ and the smaller $y.x+y=90$ and $2y-x=30$. Adding the two: $3y=120$, so $y=40$ and $x=50$. Check: 50 + 40 = 90 and $2\times 40-50=30$. 40° is the smaller angle; 60° is the familiar 30-60 complementary pair, but $2\times 30-60=0$, not 30; 30° is only the stated excess, not an angle of the pair.