Question

In figure, $OB\perp OA,\angle AOC$ and $\angle BOC$ are complementary angles . Find the value of $x$ and hence find $\angle AOC$ and $\angle BOC$.

Answer 1

In figure , we have $\angle AOC+\angle BOC={90}^{\circ }$

$\Rightarrow (x+10{)}^{\circ }+(2x+5{)}^{\circ }={90}^{\circ }$

$\Rightarrow 3x+{15}^{\circ }={90}^{\circ }$

$\Rightarrow 3x={90}^{\circ }-{15}^{\circ }={75}^{\circ }$

$\Rightarrow x={25}^{\circ }$

$\angle AOC=(25+10{)}^{\circ }={35}^{\circ }$

$\angle BOC=\left(\right(2\times 25)+5{)}^{\circ }$
$=(50+5{)}^{\circ }$
$={55}^{\circ }$
Hence, $\angle AOC={35}^{\circ }$ and $\angle BOC={55}^{\circ }$