Let one of the complementary angles = x
other angle = 90-x
Given that one of two complementary angles added to one half the other is 72. Thus
[tex](90 - x) + \frac{x}{2} = 72 \\ \\ 90 - x + \frac{x}{2} = 72 \\ \\ \frac{x}{2} - x = 72 - 90[/tex]
[tex] \frac{x - 2x}{2} = - 18 \\ \\ \frac{ - x}{2} = - 18 \\ \\ x = ( - 18) \times ( - 2) = 36[/tex]
[tex]one \: angle \: = {36}^{o} \\ \\ other \: angle = 90 - 36 = {54}^{o} [/tex]
[tex]hence \: larger \: angle \: is \: {54}^{o} [/tex]
