# Angles in ratio

The size of the angles of the triangle are in ratio x: y = 7: 5 and the angle z is 42° lower than the angle y. Find size of the angles x, y, z.

Correct result:

x =  91.4118 °
y =  65.2941 °
z =  23.2941 °

#### Solution:

5x = 7y; z = y-42; x+y+z=180

5•x = 7•y
z = y-42
x+y+z=180

5x-7y = 0
y-z = 42
x+y+z = 180

x = 1554/17 ≈ 91.411765
y = 1110/17 ≈ 65.294118
z = 396/17 ≈ 23.294118

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