SOLUTION: In △RST, m∠T is 6 more than the m∠R, and the m∠S is 9 more than the m∠T. What is the measure of each angle?
I have no idea how to do this problem a
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-> SOLUTION: In △RST, m∠T is 6 more than the m∠R, and the m∠S is 9 more than the m∠T. What is the measure of each angle?
I have no idea how to do this problem a
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Question 934151: In △RST, m∠T is 6 more than the m∠R, and the m∠S is 9 more than the m∠T. What is the measure of each angle?
I have no idea how to do this problem and it is the last question on my take-home test. Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! you need to convert every equation in terms of one variable and you can then solve for that variable.
you have:
T + S + R = 180 because the sum of the interior angles in a triangle is always equal to 180.
you have T = R + 6
you have S = T + 9
if you solve for R in the equation of T = R + 6, you will get R = T - 6.
if you solve for S in the equation of S = T + 9, you will get S = T + 9 (you're already there).
you can now convert all your angles in terms of T.
T = T
R = T - 6
S = T + 9
the sum of the angles is 180, so t + R + S = 180 becomes T + T - 6 + T + 9 = 180 degrees.
combine like terms to get 3T + 3 = 180 degrees.
subtract 3 from both sides of this equation to get 3T = 177 degrees.
divide both sides of this equation by 3 to get T = 177 / 3 = 59 degrees.
T = 59 degrees.
R = T - 6 = 53 degrees.
S = T + 9 = 68 degrees.
T + R + S = 180 becomes 59 + 53 + 68 = 180 which becomes 180 = 180 (this is good)
T = R + S becomes 59 = 53 + 6 which becomes 59 = 59 (this is good)
S = 9 + T becomes 68 = 9 + 59 which becomes 68 = 68 (this is good).
