An angle measures 42° less than the measure of a complementary angle. what is the measure of each angle?

Complimentary angles add to 90 degrees.  So if you have an angle, x, and another angle, x - 42, they should add together to equal 90...

x + x-42 = 90
2x - 42 = 90
2x = 132
x = 66 degrees (1st angle)

66 - 42 = 24 degrees (2nd angle)

 *Check  66 + 24 = 90  :)