Question 490923
We will let x be the larger angle and y be the smaller angle.
angle y = 4/5x
Now, set up two equations
4x = 5y
x + 60 = 2y
4x - 5y = 0
x  -2y = -60
-4x +8y = 240 Multiply the second equation by -4 and subtract from the first equation.
3y = 240
y = 80 degrees, which is 4/5 of x.
 x = 100 degrees.
As a check, 2(80) - 60 = 100. This does check.
Cleomenius.