Question

In the given figure, AB and CD are two lines intersecting at O. If $\angle AOC$ and $\angle BOC$ are in ratio 2 : 3, find all angles.

• A. ${72}^{\circ },{108}^{\circ },{108}^{\circ },{72}^{\circ }$
• B. ${45}^{\circ },{100}^{\circ },{100}^{\circ },{45}^{\circ }$
• C. ${30}^{\circ },{120}^{\circ },{30}^{\circ },{120}^{\circ }$
• D. ${50}^{\circ },{120}^{\circ },{50}^{\circ },{120}^{\circ }$

Answer 1

The correct option is A ${72}^{\circ },{108}^{\circ },{108}^{\circ },{72}^{\circ }$

$\angle AOC+\angle BOC={180}^{\circ }$ [Linear Pair]
$\angle AOC:\angle BOC=2:3$
Let $\angle AOC=2x$ and $\angle BOC=3x$
$\Rightarrow 2x+3x={180}^{\circ }$
$\Rightarrow 5x={180}^{\circ }$
$\Rightarrow x={36}^{\circ }$

Thus, $\angle AOC=2x={72}^{\circ }And\angle BOC=3x={108}^{\circ }$

$\angle BOD=\angle AOC={72}^{\circ }$

$\angle AOD=\angle BOC={108}^{\circ }$