SOLUTION: the second angle of a triangle measures 10 degrees more than the first angle. the third angle measures 30 degrees less than twice the second angle. what are the measures of the thr
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Question 499347: the second angle of a triangle measures 10 degrees more than the first angle. the third angle measures 30 degrees less than twice the second angle. what are the measures of the three angles? Answer by oberobic(2304) (Show Source):
You can put this solution on YOUR website! a = first angle
.
b = second angle
b = a+10 (given)
or
a = b-10
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c = third angle
c = 2b - 30
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a + b + c = 180 (because it's a triangle)
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substitute
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(b-10) + b + (2b-30) = 180
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b -10 +b +2b -30 = 180
4b -40 = 180
4b = 220
b = 55
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a = b-10
a = 45
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Therefore,
c = 180 - (55+45)
c = 80
.
Check:
2b - 30 = 2(55) - 30
= 110 - 30
= 80
True.
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Answer:
The three angles are 45, 55, and 80 degrees.
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Done.
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