SOLUTION: Two angles are supplementary. If one is 10 more than twice the other, what is the measure of both angles?

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Question 1062915: Two angles are supplementary. If one is 10 more than twice the other, what is the measure of both angles?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let x and y be the two unknown angles.


They are supplementary, so they add to 180 degrees x%2By+=+180


Solve for y to get y+=+180-x (subtract x from both sides)


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"one is 10 more than twice the other" means that


y+=+2x%2B10


Plug in y+=+180-x and solve for x


y+=+2x%2B10


180-x+=+2x%2B10 Notice how y is replaced with 180-x


180-x%2Bx+=+2x%2B10%2Bx


180+=+3x%2B10


180-10+=+3x%2B10-10


170+=+3x


3x+=+170


3x%2F3+=+170%2F3


x+=+170%2F3


x+=+56.67 This is approximate


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Now plug x+=+170%2F3 into y+=+2x%2B10 to find y


y+=+2x%2B10


y+=+2%28170%2F3%29%2B10


y+=+340%2F3%2B10


y+=+340%2F3%2B30%2F3


y+=+370%2F3


y+=+123.33 This is approximate

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We found that x+=+56.67 and y+=+123.33 approximately

So the two angle measures are approximately 56.67 degrees and 123.33 degrees