Question

An angle is $\frac{4}{5}$ of its supplement. What is its magnitude?

Answer 1

We have,

angle $\frac{4}{5}$

Let the angle be $x$

there for the compliment will be $(90-\frac{4}{5}x)$

$x=\frac{4}{5}(90-x)$

$x=72-\frac{4}{5}x$

$x+\frac{4}{5}x=72$

$\frac{5x+4x}{5}=72$

$x=72\times \frac{5}{9}$

$x=40$

the angle ${40}^o$ and its compliment is $90-40={50}^o$

Hence this is the answer.