Solving $x+2y-3=0$ and $5x+2y+12=0$, we get,

 $P=\left(-\mathrm{3,3}\right)$

Solving $x+2y-3=0$ and $x-1=0$, we get,

 $Q=\left(\mathrm{1,1}\right)$

Solving $x-1=0$ and $x-3y-4=0$, we get,

 $R=\left(1,-1\right)$

Solving $x-3y-4=0$ and $5x+y+12=0$, we get,

 $S=\left(-2,-2\right)$

$m_1=\mathrm{s}\mathrm{l}\mathrm{o}\mathrm{p}\mathrm{e}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{ }PR=-1, m_2=\mathrm{s}\mathrm{l}\mathrm{o}\mathrm{p}\mathrm{e}\mathrm{ }\mathrm{ }of\mathrm{ }\mathrm{ }QS=1$

$\Rightarrow m_1{m}_2=-1$

$\Rightarrow$ the angle between diagonals $PR$ & $QS$ is ${90}^{\mathrm{o}}$

Hence, $\left|\tan 90°\right|$ is not defined