SOLUTION: Let x◦ be the measurement of an angle. The ratio of the measurement of the complement of the angle to the measurement of the supplement of the angle is 1:3. The measurement of th

Algebra ->  Angles -> SOLUTION: Let x◦ be the measurement of an angle. The ratio of the measurement of the complement of the angle to the measurement of the supplement of the angle is 1:3. The measurement of th      Log On


   

Question 1183424: Let x◦ be the measurement of an angle. The ratio of the measurement of the complement of the angle to the measurement of the supplement of the angle is 1:3. The measurement of the complement of the angle and the measurement of the
supplement of the angle have a sum of 180◦ . Find x.
Found 2 solutions by ankor@dixie-net.com, greenestamps:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Let x◦ be the measurement of an angle.
The ratio of the measurement of the complement of the angle to the measurement of the supplement of the angle is 1:3.
%28%2890-x%29%29%2F%28%28180-x%29%29+=+1%2F3
cross multiplyL
3(90-x) = 180 - x
270 - 3x = 180 - x
270 - 180 = -x + 3x
90 = 2x
x = 45
:
The measurement of the complement of the angle and the measurement of the
supplement of the angle have a sum of 180◦ . Find x.
:
(90-x) + (180-x) = 180
90 - x + 180 - x - 180 = 0
90 = 2x
x = 45

Answer by greenestamps(13206) About Me  (Show Source):
You can put this solution on YOUR website!


The problem is strangely presented; either condition alone will give the answer.

I will use the first condition to solve the problem in a very different way from the other tutor.

The ratio of the measurement of the complement of the angle to the measurement of the supplement of the angle is 1:3. So let the measures of those two angles be y and 3y (I'm using y because the statement of the problem uses x for the measure of the angle).

The difference between the complement of an angle and the supplement of an angle is 90 degrees:

3y-y=90
2y=90
y=45

The complement of angle x is 45 degrees, so the angle x is 90-45=45 degrees.

ANSWER: The measure of the angle is 45 degrees.