Find the measure of the complement.

Question

The measure of the supplement of an angle is 14 less than 3 times the measure of the complement. Find the measure of the complement. 

 

a) 9

b) 52

c) 142

d) 38

Answer 1

Let x be the unknown angle.  Its supplement is 180-x.  Its complement is 90-x.  Its supplement is 14 less than 3 times its complement:

 

Supplement = 3(Complement) - 14

180 - x = 3(90-x) - 14

 

Solve for x.

Complement is 90 - x.

Answer 2

Convert the words into expressions/equations first.

 

Lets call the angle x. Its complement would be 90-x, and its supplement would be 180-x. 

 

supplement=3*complement-14

180-x=3*(90-x)-14

180-x=270-3x-14

194=270-2x

2x=26

x=13

 

complement =90-x=90-13=77