SOLUTION: Two angles are supplementary. One angle is 15 degrees less than 2 times the other angle. Find the measure of each angle. (Hint: The sum of the measures of supplementary angles is 1

Algebra ->  Angles -> SOLUTION: Two angles are supplementary. One angle is 15 degrees less than 2 times the other angle. Find the measure of each angle. (Hint: The sum of the measures of supplementary angles is 1      Log On


   

Question 921583: Two angles are supplementary. One angle is 15 degrees less than 2 times the other angle. Find the measure of each angle. (Hint: The sum of the measures of supplementary angles is 180 degrees.)
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

given:
Two angles are supplementary.
alpha%2Bbeta=180.........eq.1
One angle is 15 degrees less than 2 times the other angle:
alpha%2B15=2beta..........eq.2
solve the system:
alpha%2Bbeta=180.........eq.1
alpha%2B15=2beta..........eq.2
________________________________________
alpha%2Bbeta=180.........eq.1...solve for alpha
alpha=180-beta........substitute in eq.2

180-beta%2B15=2beta..........eq.2..........solve for beta

180%2B15=2beta%2Bbeta
195=3beta
65=beta

now find alpha
alpha=180-beta
alpha=180-65
alpha=115