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?

—————

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

Byou start by adding them all and setting them equal to 180 since that is half of the total degrees in a circle.(2x+8) + (3x-14) + (3x-14) = 1808x-20 = 1808x = 200x = 25