SOLUTION: I am stuck Question: One angle of a triangle is 66 degrees, the third angle is 57 degrees more than 1/2 the measure of the second angle, the sum of all the angles is 180 degrees

Algebra ->  Angles -> SOLUTION: I am stuck Question: One angle of a triangle is 66 degrees, the third angle is 57 degrees more than 1/2 the measure of the second angle, the sum of all the angles is 180 degrees      Log On


   

Question 988110: I am stuck
Question: One angle of a triangle is 66 degrees, the third angle is 57 degrees more than 1/2 the measure of the second angle, the sum of all the angles is 180 degrees. What is the measure of the second angle? What is the measure of the third angle?
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!


first angle of a triangle is alpha=highlight%2866+%29degrees
the second angle is beta
the third anglegamma is 57 degrees more than 1%2F2 the measure of the second angle beta: so the third angle is gamma=%281%2F2%29beta%2B57
the sum of all is 180 degrees:
alpha%2Bbeta%2Bgamma=180....substitute 66 for alpha and %281%2F2%29beta%2B57 for gamma
66%2Bbeta%2B%281%2F2%29beta%2B57=180......solve for beta
2beta%2F2%2B%281%2F2%29beta%2B123=180
%283%2F2%29beta=180-123
%283%2F2%29beta=57
3beta=57%2A2
3beta=114
beta=114%2F3
beta=38->the second angle
the third angle will be gamma=%281%2F2%29beta%2B57=>gamma=%281%2F2%29%2A38%2B57=>gamma=19%2B57=>gamma=76


so,
the measure of the second angle is highlight%2838%29 degrees
the measure of the third angle is highlight%2876%29 degrees