SOLUTION: the ratio of an angle to its complement is 2:7. What is the ratio of the angle to its supplement.

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Question 501361: the ratio of an angle to its complement is 2:7. What is the ratio of the angle to its supplement.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
An angle and its complement always have a sum of 90 degrees
the ratio of an angle to its complement is 2%3A7...-> alpha%3A%2890-alpha%29=2%3A7
An angle and its supplement always have a sum of 180 degrees
you want to set this up as a proportion.
2+%2F+7+=+x+%2F+%2890+-x%29
2%2890+-x%29+=+7x
180-2x+=7x
9x+=+180
x+=+20
90+-20+=+70
70 degrees + it's supplement, 120 degrees exist in a 7%3A12 ratio
The compliment of 20 is 90-20 or 70 degrees
20+%2F+70 is a ratio of 2%3A7