The measures of two complementary angles have a ratio of 3 : 2. what is the measure of the larger angle?

Question:

The measures of two complementary angles have a ratio of 3 : 2. What is the measure of the larger angle?

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Solution:

Call those two angles  x  and  y, where  x  is the larger one.

If they are complementary, then their sum equals  90°:

x + y = 90°      (i)

Also, the ratio between  x  and  y  is  3 : 2, so

  x           3
——  =  ——
  y           2

Product of the extremes = product of the means:

2x = 3y

2x – 3y = 0        (ii)

Now, just solve this system of equations:

  x  +  y = 90°         (i)
2x – 3y =   0          (ii)

Solve it with elimination. Since you want to know the value of the larger angle, which is  x, then eliminate the variable  y  by doing the following:

Multiply the equation  (i)  by  3,

3x + 3y = 270°        (iii)
2x – 3y =     0          (ii)

then add both equations, so you cancel out the variable  y:

3x + 2x + 3y – 3y = 270° + 0

3x + 2x = 270°

5x = 270°

         270°
x  =  ———
           5

x = 54°    <———  this is the measure of the larger angle.

I hope this helps. =)

Tags:  system of linear equations elimination method solve complementary angles algebra geometry