If  two supplementary angles are in the ratio $2:3$ , then the complement of smaller angle is  

Total number of parts$=2+3=5$

Required supplementary angles are$\frac{2}{5}\times 180°,\frac{3}{5}\times 180°$

$=\frac{2\times 180}{5},\frac{3\times 180°}{5}$

$=2\times 36°,3\times 36°$

$=72°,108°$

Smaller angle=$72°$ ,

$\therefore$ compliment of smaller angle is$=90°-72°=18°$