Question

If an angle differ from its complement by ${10}^{\circ }$, find the angle.

Answer 1

Let required angle = $x^{\circ }$
Then its complement angle = ${90}^{\circ }-x^{\circ }$
$\therefore x-({90}^{\circ }-x)=10$
$\Rightarrow x-{90}^{\circ }+x={10}^{\circ }\Rightarrow 2x={10}^{\circ }+{90}^{\circ }={100}^{\circ }$
$\therefore x=\frac{{100}^{\circ }}{2}={50}^{\circ }$
$\therefore$ Required angle = ${50}^{\circ }$