SOLUTION: Angles - The sum of the measures of three angles in a triangle is 180 degrees. The measure of one angle of a triangle is one degree more than three times the measure of the smalles

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Question 611112: Angles - The sum of the measures of three angles in a triangle is 180 degrees. The measure of one angle of a triangle is one degree more than three times the measure of the smallest angle. The measure of the third angle is 13 degrees less than twice the measure of the second angle. Find the measure of each angle.
(now the back of the book says the answers are 19 degree, 58 degree, & 103 degree)but I don't know how they got them.
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
Let x, y and z be the three angles. And let x be the smallest of the 3
x+%2B+y+%2B+z+=+180
y+=+3x+%2B+1
z+=+2y+-+13
So let's plug in and simplify
x+%2B+y+%2B+z+=+180
x+%2B+%283x%2B1%29+%2B+%282y-13%29+=+180
4x%2B1+%2B+2%283x%2B1%29+-+13+=+180
4x+-+12+%2B+6x+%2B+2+=+180
10x+-10+=+180
10x+=+190
x+=+19
Now use that value for x to solve for y and z using the 2nd and third equations above
y+=+3%2A19+%2B+1
y+=+58
you can do the last one