Question

In the given figure,
If $\angle AOB=\angle BOC=\angle COD={38}^{\circ }$,
find reflex angle $\angle AOC$ and reflex angle $\angle AOD$.

Answer 1

Given, $\angle AOB=\angle BOC=\angle COD={38}^{\circ }$.

Now, $\angle AOC=\angle AOB+\angle BOC$

$={38}^{\circ }+{38}^{\circ }={76}^{\circ }$

$⟹\angle AOC={76}^{\circ }$

Then, reflex angle $\angle AOC={360}^{\circ }-{76}^{\circ }={284}^{\circ }$.

Now, $\angle AOD=AOB+\angle BOC+\angle COD$

$={38}^{\circ }+{38}^{\circ }+{38}^{\circ }={114}^{\circ }$

$⟹\angle AOD={114}^{\circ }$.

Then, reflex angle $\angle AOD={360}^{\circ }-{114}^{\circ }$ $={246}^{\circ }$.