SOLUTION: In a triangle, the measures of the first angle is three times the measure of the second angle decreased by 50 degrees. The measure of the third angle is 25 degrees less than second

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Question 1136934: In a triangle, the measures of the first angle is three times the measure of the second angle decreased by 50 degrees. The measure of the third angle is 25 degrees less than second angle. What is the measure of each angle?
Found 2 solutions by josgarithmetic, Theo:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
first                  3x-50
second                   x
third or last           x-25
SUM                       180


%283x-50%29%2Bx%2B%28x-25%29=180
-
5x-75=180
5x=255
x=51
.
.

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
let A be the first angle and B be the second angle and C be the third angle.

A = 3B - 50
C = B - 25

A + B + C = 180 becomes 3B - 50 + B + B - 25 = 180

combine like terms to get 5B - 75 = 180

add 75 to both sides of the equation to get 5B = 255

solve for B to get B = 255 / 5 = 51.

A = 3B - 50 = 3 * 51 - 50 = 153 - 50 = 103

C = B - 25 = 51 - 25 = 26

the angles are A = 103 and B = 51 and C = 26

A + B + C = 103 + 51 + 26 = 180
103 = 3 * 51 - 50 = 153 - 50 = 103
26 = 51 - 25 = 26

all problem statements are confirmed to be satisfied, confirming the solution is good.

the solution is measure of the first angle is 103 and measure of the second angle is 51 and measure of the third angle is 26.