# Angles of the triangle

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

Correct result:

α =  36 °
β =  63 °
γ =  81 °

#### Solution:

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

a = 36
b = 63
c = 81

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