$\cos(\overrightarrow{a},\overrightarrow{b})$
$=\dfrac{\overrightarrow{a}.\overrightarrow{b}}{|\overrightarrow{a}|.|\overrightarrow{b}|}$
$=\dfrac{-1.2+1.0}{\sqrt{1^2+1^2}.\sqrt{2^2}}$
$=\dfrac{-1}{\sqrt2}$
$\Rightarrow (\overrightarrow{a},\overrightarrow{b})=135^o$