Question

one of two complementary angles added to one half the other is 72°. Find the measure of the larger angle.

Answer 1

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

`(90 - x) + (x)/(2) = 72 \\ \\ 90 - x + (x)/(2) = 72 \\ \\ (x)/(2) - x = 72 - 90`


`(x - 2x)/(2) = - 18 \\ \\ ( - x)/(2) = - 18 \\ \\ x = ( - 18) * ( - 2) = 36`

`one \: angle \: = {36}^(o) \\ \\ other \: angle = 90 - 36 = {54}^(o)`


`hence \: larger \: angle \: is \: {54}^(o)`