The acute angle between lines 6 x 2 + 11 x y - 10 y 2 = 0 is

Acute angle between pair of straight lines $a{x}^2+2hxy+b{y}^2=0$ is given by $\tan \theta =\left|\frac{2\sqrt{h^2-ab}}{a+b}\right|$

By comparing the given equation of lines with $a{x}^2+2hxy+b{y}^2=0$ we get

$a=6,b=-10,h=\frac{11}{2}$

Then, $\tan \theta =\left|\frac{2\sqrt{{\displaystyle \frac{121}{4}}+60}}{-4}\right|=\left|\frac{\sqrt{361}}{-4}\right|$

$\Rightarrow \theta ={\tan }^{-1}\left(\frac{\sqrt{361}}{4}\right)$