An angle measures 26 degrees more than 3 times its complement. Find the measure of its complement

Question

 An angle measures 26 degrees more than 3 times its complement. Find the measure of its complement

Answer 1

Let x be the angle being discussed. By definition, two angles are complementary if they add to 90 degrees. So, the complement of angle x is (90-x). So, our equation is

 

 

x=26+3(90-x)

 

x=26+270-3x

 

4x=296

 

x=74

 

So, the complement of angle x is (90-74)=16 degrees\

 

check: 74=26+3(16)

          74=26+48

          74=74      yes!

 

Answer 2

If possible, assign a variable to the value the problem asks us to find ("the measure of it's complement").  Let C=measure of complementary angle

 

Note:   an angle + complement = 90°

           complement = 90° - angle

 

          C = 90 - (26 + 3C)      (substitute "26 more than 3 times it's complement" in place of 'angle')

          4C = 64              (collect terms)

           C = 16               (divide both sides by 4)

 

Checking (very important):

    Is  (26 +3(16)) + (16) = 90       ?        ("angle is 26 more than 3*complement")

          26 + 48 + 16 = 90  ?

                 90 = 90   ?  yes!