SOLUTION: In a triangle one angle is 23 degrees more than the smallest angle the third angle is 10 degrees more than the sum of the other two angles find the measurement of each angle I

Question 283663: In a triangle one angle is 23 degrees more than the smallest angle the third angle is 10 degrees more than the sum of the other two angles find the measurement of each angle

I can not figure out how to write this problem out my book has nothing like it and I cant find it online PLEASE HELP
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
The triangle has 3 angles: a, b, and c.
We know that a + b + c = 180 degrees because all triangles have 180 degrees.
.
We'll pick 'a' as the smallest angle.
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b = a + 23 :: given
.
c = a+b+10 :: given
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So, it seems we have 3 unknowns and not enough equations to solve them.
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But let's think about it.
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We have
a = a
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b = a+23
.
c = a+b+10
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for 'c', substitute b=a+23
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c = a + (a+23) +10
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a + b + c = 180,
so...
a + (a+23) + (a+(a+23)+10) = 180
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4a + 56 = 180
4a = 124
a = 31
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b = a +23
b = 31+23 = 54
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c = a + b + 10
c = 31 + 54 + 10 = 95
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Do they add up to 180?
31 + 54 + 95 = 180
Correct.
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The three angles are: 31, 54, and 95.
.
Done.
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