Question

An angle is equal to 8 times its complement. Determine its measure.

Answer 1

Let the required angle =x
Then its complement angle =${90}^{\circ }-x\therefore x=8({90}^{\circ }-x)\Rightarrow x=720-8x\Rightarrow x+8x={720}^{\circ }\Rightarrow 9x={720}^{\circ }\Rightarrow x=\frac{{720}^{\circ }}{9}={80}^{\circ }$
$\therefore$ Required angle =${80}^{\circ }$