Question

An angle is equal to five times its complement. Determine its measure.

Answer 1

Let required measure of angle = $x^0$
$\therefore$ Its complement angle = ${90}^0-x$
$\therefore x=5({90}^0-x)\Rightarrow x={450}^0-5x$
$\Rightarrow x+5x={450}^0\Rightarrow 6x={450}^0$
$\Rightarrow x=\frac{{450}^0}{6}={75}^0$
$\therefore$ Required angle = ${75}^0$