So,
We know that the sum of the angles in a triangle will always equal 180°.
x + y + z = 180
\(y= \frac{1}{3}x\)
\(z= \frac{2}{3} x\)
We can substitute 1/3x for y and 2/3x for z in the first equation.
\(x+ \frac{1}{3} x+ \frac{2}{3}x=180\)
Collect Like Terms.
2x = 180
Divide both sides by 2.
x = 90
Substitute in the second equation.
\(y= \frac{1}{3}(90)\)
y = 30
Substitute in the third equation.
\(z= \frac{2}{3} (90)\)
z = 60
Let's check our values.
x = 90
y = 30
z = 60
x + y + z = 180?
90 + 30 + 60 = 180?
90 + 90 = 180?
180 = 180 YES!
This checks.
The first angle is 90°, the second angle is 30°, and the third angle is 60°.
