Angles in ratio

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

Correct answer:

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

Step-by-step explanation:


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

Row 3 - 1/5 · Row 1 → Row 3
5x-7y = 0
y-z = 42
2.4y+z = 180

Pivot: Row 2 ↔ Row 3
5x-7y = 0
2.4y+z = 180
y-z = 42

Row 3 - 1/2.4 · Row 2 → Row 3
5x-7y = 0
2.4y+z = 180
-1.417z = -33


z = -33/-1.41666667 = 23.29411765
y = 180-z/2.4 = 180-23.29411765/2.4 = 65.29411765
x = 0+7y/5 = 0+7 · 65.29411765/5 = 91.41176471

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

Our linear equations calculator calculates it.



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