Magnitudes 24271

In the ABC triangle, the magnitude of the inner angle beta is one-third the magnitude of the angle alpha and 20 ° larger than the magnitude of the gamma angle. Determine the magnitudes of the interior angles of this triangle.

Correct answer:

A =  120
B =  40
C =  20

Step-by-step explanation:


B=A/3
B = 20+C
A+B+C=180

A-3B = 0
B-C = 20
A+B+C = 180

Row 3 - Row 1 → Row 3
A-3B = 0
B-C = 20
4B+C = 180

Pivot: Row 2 ↔ Row 3
A-3B = 0
4B+C = 180
B-C = 20

Row 3 - 1/4 · Row 2 → Row 3
A-3B = 0
4B+C = 180
-1.25C = -25


C = -25/-1.25 = 20
B = 180-C/4 = 180-20/4 = 40
A = 0+3B = 0+3 · 40 = 120

A = 120
B = 40
C = 20

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