SOLUTION: The sum of the measures of the angles of any triangle is 180 degrees . In a certain triangle, the largest angle measures 55degrees less than twice the medium angle, and the smalle

Question 230559: The sum of the measures of the angles of any triangle is 180 degrees . In a certain triangle, the largest angle measures 55degrees less than twice the medium angle, and the smallest angle measures 25 degrees less than the medium angle. Find the measures of each of the three angles.
Answer by checkley77(12844) (Show Source): You can put this solution on YOUR website!
X+Y+Z=180
Z=2Y-55
X=Y-25
REPLACE X IN THE FIRST EQUATION BY (Y-25) & REPLACE Z BY(2Y-55) & SOLVE FOR Y
Y-25+Y+2Y-55=180
4Y=180+55+25
4Y=260
Y=260/4
Y=65 DEGREES FOR THE MEDIUM ANGLE.
X=65-25=40 DEGREES FOR THE SMALLEST ANGLE.
Z=2*65-55
Z=130-55
Z=75 DEGREES FOR THE LARGEST ANGLE.
PROOF:
40+65+75=180
180=180
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