Magnitudes 3304

In triangle ABC, the interior angle at vertex B is 10 degrees greater than the angle at vertex A, and the angle at vertex C is three times greater than the angle at vertex B. Calculate the magnitudes of the interior angles of the triangle.

Correct answer:

A =  28
B =  38
C =  114

Step-by-step explanation:


B=10+A
C = 3·B
A+B+C=180

A-B = -10
3B-C = 0
A+B+C = 180

Row 3 - Row 1 → Row 3
A-B = -10
3B-C = 0
2B+C = 190

Row 3 - 2/3 · Row 2 → Row 3
A-B = -10
3B-C = 0
1.667C = 190


C = 190/1.66666667 = 114
B = 0+C/3 = 0+114/3 = 38
A = -10+B = -10+38 = 28

A = 28
B = 38
C = 114

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