Question

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

Answer 1

\[\theta_2 = 3\theta_1+4\]
\[\theta_3 = 6\theta_1-4\]
we know that for a triangle
\[\theta_1+\theta_2+\theta_3=180\]
\[\theta_1+3\theta_1+4+6\theta_1-4=180\]
\[10\theta_1=180 \Rightarrow \theta_1=18\]
\[\Rightarrow \theta_2 = 3\theta_1+4=58\]
\[\Rightarrow \theta_3 = 6\theta_1-4=104\]

Answer 2

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