Question

an angle is 4/5 of its complement. what is its magnitude

Answer 1

x= 4/5(90-x)
x= 72-4x/5
x+4x/5 = 72
5x = 360
x= 72

Answer 2

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$Let \: the \: angle \: be \: x. \\ Therefore \: Its \: compliment \: will \: be \: (90- \frac{4}{5}x). \\ \\According \: to \: the \: question,$

$x = \frac{4}{5}(90-x) \\ \implies = x = 72 - \frac{4}{5}x \\ \implies x + \frac{4}{5}x = 72 \\ \implies \frac{5x+4x}{5} = 72 \\ \implies \frac{9}{5}x = 72 \\ \implies x = 72 \times \frac{5}9 = 40$

Hence, the angle is 40° and its compliment is 90-40 = 50°....