# Angles of the triangle

ABC is a triangle. The size of the angles alpha and beta are in a ratio of 4:7. The angle gamma is greater than the angle alpha by a quarter of a straight angle. Determine angles of the triangle ABC.

α =  36 °
β =  63 °
γ =  81 °

### Step-by-step explanation:

7a = 4b; c = a+1/4 · 180; a+b+c=180

7·a = 4·b
c = a+1/4 · 180
a+b+c=180

7a-4b = 0
4a-4c = -180
a+b+c = 180

Row 2 - 4/7 · Row 1 → Row 2
7a-4b = 0
2.286b-4c = -180
a+b+c = 180

Row 3 - 1/7 · Row 1 → Row 3
7a-4b = 0
2.286b-4c = -180
1.571b+c = 180

Row 3 - 1.57142857/2.28571429 · Row 2 → Row 3
7a-4b = 0
2.286b-4c = -180
3.75c = 303.75

c = 303.75/3.75 = 81
b = -180+4c/2.28571429 = -180+4 · 81/2.28571429 = 63
a = 0+4b/7 = 0+4 · 63/7 = 36

a = 36
b = 63
c = 81

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