Let x represent the measurment of an acute angle in degrees. the ratio of the complement of x to the supplement of x is 2: 5. guess and check to determine the value of x. explain why your answer is correct.

Ratio of complement of x : supplement of x 
2 : 5
⇒ 2 times the supplement of x will be equal to 5 times the complement of x

5(90 - x) = 2 (180 - x)
450 - 5x = 360 - 2x
5x - 2x = 450 - 360
3x = 90
x = 30°

Complement of x = 90 - x = 90 - 30 = 60
Supplement of x = 180 - x = 180 - 30 = 150
Ratio:
60 : 150
60 ÷ 30 : 150 ÷ 30
2 : 5 (checked)