let x represent the measurement of an acute angle in degrees.The ratio of the complement of x to the supplement of x is 2:5.Guess to determine the value of x.

Question

and explain why you got the awnser. That is the question but i dot understand it HELP ME SOLE IT PLEASE

Answer 1

Hi Kelly

 

Since we've discussed complement and supplement angles already

 

Let x represent the acute angle

 

Then (90 - x) is its complement and (180 - x) is its supplement.

If we set up the ratio as given in the statement, then (90 - x) / (180 - x) = 2/5.

 

Solve for x.  I don't know why the problem statement wants you to guess.

Answer 2

x is an acute angle, therefore, less than 90 degrees.

x plus the complement of x is equal to 90 degrees.  This tells us that the complement of x is also an acute angle.

x plus the supplement of x is equal to 180 degrees.  This tells us that the supplement of x is an obtuse angle.

Finally, we know that the complement of x to the supplement of x has a 2/5 ratio.

 

Let x,(90-x),(180-x) represent the angle, the complement of the angle, and the supplement of the angle.

 

2  =  (90-x)

5      (180-2)

 

2(180-x) = 5(90-x)  cross multiplying

 

360 - 2x = 450 - 5x

      + 5x =      + 5x  moving all x's to the left

360 + 3x = 450

 

360 + 3x = 450

-360       = -360  leaving all non x's to the right

 

3x = 90

3  =  3

 

x = 30

 

By the way, checking our answer the complement would be 60 degrees and the supplement would be 150 degrees and 

60  =  2

150    5

 

Hope that makes sense.