Largest angle of the triangle

What is the largest angle of the triangle if the second angle is 10° greater than twice the first and the third is 30° smaller than the second?

Correct answer:

B =  86 °

Step-by-step explanation:


A+B+C=180
B = 10 + 2·A
C = B-30

A+B+C = 180
2A-B = -10
B-C = 30

Pivot: Row 1 ↔ Row 2
2A-B = -10
A+B+C = 180
B-C = 30

Row 2 - 1/2 · Row 1 → Row 2
2A-B = -10
1.5B+C = 185
B-C = 30

Row 3 - 1/1.5 · Row 2 → Row 3
2A-B = -10
1.5B+C = 185
-1.667C = -93.333


C = -93.33333333/-1.66666667 = 56
B = 185-C/1.5 = 185-56/1.5 = 86
A = -10+B/2 = -10+86/2 = 38

A = 38
B = 86
C = 56

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