Let x be a number, we know that the angles are in ratio 2:3, this means that one of the angles is 2x and the other is 3x. We also know that they are complementary angles hence we have the equation:
[tex]2x+3x=90[/tex]Solving for x we have:
[tex]\begin{gathered} 2x+3x=90 \\ 5x=90 \\ x=\frac{90}{5} \\ x=18 \end{gathered}[/tex]Therefore the larger angle is:
[tex]3(18)=54[/tex]