Triangle angles

Calculate the size of the interior angles of a triangle if the size of the second angle is 120 degrees less than twice the size of the first angle and the size of the third angle is equal to the difference between the sizes of the first and second angles.

Final Answer:

A =  90
B =  60
C =  30

Step-by-step explanation:


B=2·A-120
C = A-B
A+B+C=180

2A-B = 120
A-B-C = 0
A+B+C = 180

Row 2 - 1/2 · Row 1 → Row 2
2A-B = 120
-0.5B-C = -60
A+B+C = 180

Row 3 - 1/2 · Row 1 → Row 3
2A-B = 120
-0.5B-C = -60
1.5B+C = 120

Pivot: Row 2 ↔ Row 3
2A-B = 120
1.5B+C = 120
-0.5B-C = -60

Row 3 - -0.5/1.5 · Row 2 → Row 3
2A-B = 120
1.5B+C = 120
-0.667C = -20


C = -20/-0.66666667 = 30
B = 120-C/1.5 = 120-30/1.5 = 60
A = 120+B/2 = 120+60/2 = 90

A = 90
B = 60
C = 30

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