## anonymous 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

$\theta_2 = 3\theta_1+4$ $\theta_3 = 6\theta_1-4$ 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

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