Question

the measure of angle a is 16 degrees greater than the measure of angle b. the tow angles are complementary. find the measure of each angle

Answer 1

This is a system of equations problem.  Set up the 2 equations like so: If the angles are complementary then they add up to 90, therefore, a + b = 90.  We also know that a is 16 more than b.  The word "is" means equals and "more" is addition.  Therefore, a is 16 more than b is "a = b + 16".  Now sub in that value of a (b + 16) into the first equation and solve for b.  Then back-substitute to solve for a. (b + 16) + b = 90 so 2b + 16 =  90 and 2b = 74.  So b = 37.  If b = 37, then a + 37 = 90 and a = 53.  Check yourself to make sure that 37 + 53 add up to equal 90 (they do, just get used to checking yourself for accuracy).