The ratio of the measure of an angle to its complement is 4:11. Find the ratio of the measure of the angle to the measure of its supplement.

Question

Write your answer as a reduced ratio a:b

Answer 1

4 : 11 :: x : (90 - x)              proportion

11x = 4(90 - x)                    product means/extremes

11x = 360 - 4x                    distribute

15x = 360                           add 4x to both sides

x = 24                                divide both sides by 15

 

What is the ratio of this angle to its supplement?

Answer 2

Let x = degree measure of the angle

 

So, the complement of the angle has degree measure 90-x

 

4/11 = x/(90-x)

 

4(90-x) = 11x

 

360 - 4x = 11x

 

15x = 360

 

x = 24°

 

Supplement = 180 - x = 156°

 

x/(180-x) = 24/156 = 2/13