SOLUTION: If the ratio of the measures of the complementary angle to that of the supplementary angle of the given angle is 1:10, find the ratio of the given angle with its complementary angl

Algebra ->  Angles -> SOLUTION: If the ratio of the measures of the complementary angle to that of the supplementary angle of the given angle is 1:10, find the ratio of the given angle with its complementary angl      Log On


   

Question 554434: If the ratio of the measures of the complementary angle to that of the supplementary angle of the given angle is 1:10, find the ratio of the given angle with its complementary angle?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
cx = complement of x
sx = supplement of x
cx/sx = 1/10
this makes:
10cx = sx
cx = 90-x
sx = 180-x
this makes:
10cx = sx become:
10(90-x) = 180-x
simplify to get:
900 - 10x = 180 - x
add 10x to both sides of this equation and subtract 180 from both sides of this equation to get:
9x = 720
divide both sides of this equation by 9 to get:
x = 80.
your angle is 80 degrees.
the complement to this angle is 10 degrees.
the supplement to this angle is 100 degrees.
the ratio of the complement to the supplement is 1/10.
this confirms the angle is good.
the ratio of the angle to it's complement is equal to
80/10 = 8/1.