2. Acute angle between lines x² + 4xy + y² = 0 is tan^-1(3)^1/2 = pi / 3

Angle bisectors of x² + 4xy + y² = 0 are given by

x² - y² = xy

 1 - 1       2

or, x = + y

As, x + y = 0 is perpendicular to x - y = 4, given triangle is isosceles with vertical angle equal to pi / 3 and hence it is equilateral.