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  • 5 years ago

The second angle of a triangle is 4° larger than three times the first angle. The third angle is 4° smaller than six times the first angle. Find the measure of each angle. Write your answers in the order of 1st angle, 2nd angle, 3rd angle

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  1. sgadi
    • 5 years ago
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    \[\theta_2 = 3\theta_1+4\] \[\theta_3 = 6\theta_1-4\] we know that for a triangle \[\theta_1+\theta_2+\theta_3=180\] \[\theta_1+3\theta_1+4+6\theta_1-4=180\] \[10\theta_1=180 \Rightarrow \theta_1=18\] \[\Rightarrow \theta_2 = 3\theta_1+4=58\] \[\Rightarrow \theta_3 = 6\theta_1-4=104\]

  2. anonymous
    • 5 years ago
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    Let x denote the first angle, y denote the second angle and z denote the third angle. So from the first sentence: 3x+4= y From the second sentence. 6x-4=z Now, you have 3 unknowns and 2 equations, so you need one more equation. Using the property of a triangle, you know the angles must add up to 180. So, x+y+z=180 Solving the system will yield x=18, y=58,z=104

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