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.

Final Answer:

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

Step-by-step explanation:

$$\begin{gathered} x:y=7:5 \\ 5x=7y \\ z=y-42{}^{\circ } \\ x+y+z=180{}^{\circ } \\ x+y+(y-42)=180 \\ x+2y-42=180 \\ x+2\cdot \frac{5}{7}\cdot x-42=180 \\ x+2\cdot 5/7\cdot x-42=180 \\ 17x=1554 \\ x=\frac{1554}{17}=91.41176471 \\ x=\frac{1554}{17}\doteq 91.411765=91.4118^{\circ }=91°24^{\prime }42" \end{gathered}$$

$y=\frac{5}{7}\cdot x=\frac{5}{7}\cdot 91.4118=65.2941^{\circ }=65°17^{\prime }39"$

$z=y-42=65.2941-42=23.2941^{\circ }=23°17^{\prime }39"$

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