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 $\angle BOC$. [3 MARKS]

Answer 1

Concept: 1 Mark
Application: 0.5 Mark
Answer: 0.5 Marks each

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

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

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

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

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

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

$\angle BOC=(2\times 25+5{)}^{\circ }={55}^{\circ }$