The difference of two complementary angles is 30 degrees. Find the measures of the angles.

60 degrees and 30 degrees

Step-by-step explanation:

let the angles be x and y

we are given that the angles are complementary (i.e they sum up to 90 degrees). Hence we can write the first equation:

x + y = 90 (eq 1)

we are also given that the difference between the two angles is 30 degrees). Similarly we can write

x - y = 30 (eq 2)

now we have a system of 2 equations with 2 unknowns, which we can solve by elimination:

eq 1 + eq 2:

(x + y) + (x - y) = 90 + 30

2x = 120  (divide both sides by 2)

x = 120/2

x = 60 deg (substitute this back into eq 1)

x + y = 90

60 + y = 90 (subtract 60 from both sides)

y = 90 - 60

y = 30 deg.