Question

In the figure, ray OC stands on the line AB and $\angle BOC:\angle AOC=2:7$. Find the angles $\angle AOC$ and $\angle BOC$. [3 MARKS]

Answer 1

Concept: 1 Mark
Application: 2 Marks

$\angle BOC:\angle AOC=2:7$ (Given)

$\angle BOC+\angle AOC={180}^{\circ }$

Let $\angle BOC=2x^{\circ }$ and $\angle AOC=7x^{\circ }$

Then $2x^{\circ }+7x^{\circ }={180}^{\circ }$

$9x={180}^{\circ }$

$x={20}^{\circ }$

Now, $\angle BOC=2\times {20}^{\circ }={40}^{\circ }$

$\angle AOC=7\times {20}^{\circ }={140}^{\circ }$

Hence, $\angle AOC={140}^{\circ }$ and $\angle BOC={40}^{\circ }$