If two supplementary angles are in the ratio $1:4$  then the angles are $30°,120°$ .

Total number of parts$=5$

Supplementary angles are$\frac{1}{5}\times 180°,\frac{4}{5}\times 180°$

                                               $\begin{array}{c}=\frac{180°}{5},\frac{4\times 180°}{5}\\ =36°,4\times 36°\\ =36°,4\times 36°\\ =36°,144°\end{array}$

$\therefore$ statement-1 is false

II) If sum of two angles is $90°$ , then angles are said to be complementary angles.

$\therefore$ statement-2 is true.