The measure of ∠a is 6° greater than the measure of ∠b. the two angles are complementary. find the measure of each angle.

Let's say the measure of angle b = B. The measure of angle A is 6° greater, making A = B + 6.

Since they are complementary, angles A and B must add to 90°. Make an equation:
A + B = 90

And solve it for B, substituting B+6 in for angle A:
A + B = 90
B + 6 + B = 90
2B + 6 = 90
2B = 84
B = 42°

Now you know B = 42°. Find A using A = B + 6. Since A is 6° greater than B, that makes A = 42° + 6° = 48°. 



A = 48°
B = 42°