A triangle has 3 angles of 60 degrees, (5y-40) degrees, and (2y+20) degrees. Show that the triangle is equilateral.

All the angles in a triangle add up to 180 degrees.

Therefore, 60 + (5y - 40) + (2y + 20) = 180.

This can be simplified to 7y +40 = 180.

And simplified again to 7y = 140, which then means y = 140 / 7 = 20 degrees.

The first angle is 60 degrees, the second angle is 5x20-40=60 degrees, the third angle is 2x20+20=60 degrees. 

Since all three angles are 60 degrees it must be an equilateral triangle.